criteria for materiality decisions in accounting a
TRANSCRIPT
CRITERIA FOR MATERIALITY DECISIONS IN ACCOUNTING
A STATISTICAL APPROACH
by
HAMED MOHAMAD HADIDI, B. of Com., M.B.A.
A DISSERTATION
IN
BUSINESS ADMINISTRATION
Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for
the Degree of
DOCTOR OF BUSINESS ADMINISTRATION
Tv3
ACKNOWLEDGMENTS
I am deeply indebted to Professor Doyle Z. Williams
for his direction of this dissertation and to the other mem
bers of my committee. Professors Howard L. Balsley and M.
Herschel Mann, for their helpful criticism.
1 1
CONTENTS
• •
ACKNOWLEDGMENTS 11
LIST OF TABLES vi
LIST OF ILLUSTRATIONS viii
I. INTRODUCTION 1
General Statement of the Problem . . . . 1
Definition and Uses of
Materiality 2
Judgment Based Materiality 6
Inadequate Materiality Guidelines . 7
State of the Art 9
AICPA Approach 9
SEC Approach 9
Approaches in Accounting Literature 10
Scope of the Study 11
Statement of the Problem 11
Nature and Purpose of the Study . . 13
Organization of the Study 16
II. METHODOLOGY 17
Review of the Literature 17
AICPA Approach 19
SEC Approach 21
Approaches in Accounting Literature 22 • > •
111
IV
Factor Analysis and Research Design. . . 29
The Factor Model 30
The Variables 31
The Data 32
The Population 33
The Collection and Tabulation
of Data 33
The Nximber of Factors 35
The Rotation of the Axes 36
The Criteria Based on Factor Analysis. . 38
Summary 48
III. FACTOR ANALYSIS 50
Introduction 50
Importance of Variations in the Data . . 52
Uses of Factor Analysis 53
Criticism of Factor Analysis 54
Models of Factor Analysis 55
Correlation Matrix 56
Centroid Method of Factor Extraction . . 58
Rotation of the Axes 63
Summary 69
IV. FACTOR ANALYSIS RESULTS AND MATERIALITY CRITERIA 71
Introduction 71
Data Compilation 72
Factor Analysis of the Data 74
V
Materiality Criteria Based on Factor Analysis Results 90
Groups' Contributions to Net
Income 91
Groups' Absolute Sums 93
Groups' Equalized Effects on Net
Income 94
Groups' Multiples 96
Maximum Allowable Departure from
Standard Practice 97
Percentage Materiality Criteria. . . 99
Applicability of Materiality Criteria 101 Materiality Criteria in a Range
Form 102
Summary 108
V. SUMMARIES AND LIMITATIONS 110
Deficient Materiality Guidelines 110
Application of Factor Analysis Ill
Criteria Based on Factor Analysis . . . . 113
Single-Point Materiality Criteria. . 114
Range Form Materiality Criteria. . . 115
Limitations of the Study 116
Recommendations 118
BIBLIOGRAPHY 121
APPENDIX 124
Significance of Sample r 125
The Questionnaire and Results Summary 127
Sample Size in the Study 129
LIST OF TABLES
Table Page
1. Illustrative Correlation Matrix of Seven Hypothetical Variables 58
2. Unrotated Three Centroid Factor Loadings Extracted From the Illustrative Correlation Matrix Presented in Table 1, and Their Corresponding Eigenvalues 60
3. Obliquely Rotated Three Centroid Factor Loadings Extracted From the Illustrative Correlation Matrix Presented in Table 1 . . 65
4. Highest Loadings of Seven Hypothetical Variables on Obliquely Rotated Three Factors Extracted From the Illustrative Correlation Matrix Presented in Table 1 68
5. Empirical Correlation Matrix of Selected Twenty Income Statement Accounts in the Retail Trade Industry 75
6. Unrotated Seven Principal Factor Loadings Extracted From the Empirical Correlation Matrix Presented in Table 5, and Their Corresponding Eigenvalues 77
7. Varimax Rotated Seven Principal Factor Loadings Extracted From the Empirical Correlation Matrix Presented in Table 5 . . 79
8. Clusters of Selected Twenty Income Statement Accounts on Seven Principal Factors Extracted From the Empirical Correlation Matrix Presented in Table 5 80
9. Unrotated Five Principal Factor Loadings Extracted From the Empirical Correlation Matrix Presented in Table 5, and Their Corresponding Eigenvalues 81
vi
VI1
Table Page
10. Varimax and Obliquely Rotated Five Principal Factor Loadings Extracted From the Empirical Correlation Matrix Presented in Table 5 82
11. Clusters of Selected Twenty Income Statement Accounts on Five Principal Factors Extracted From the Empirical Correlation Matrix Presented in Table 5 83
12. Highest Loadings of Selected Twenty Income Statement Accounts on Varimax and Obliquely Rotated Five Factors Extracted From the Empirical Correlation Matrix Presented in Table 5 88
13. Net Contributions of the Five Groups of Accounts to Business Net Income 9 3
14. Absolute Sum of the Arithmetic Means of the Five Groups of Accounts 94
15. Equalized Effects of the Five Groups on Net Income 9 5
16. Transforming Groups' Multiples to Percentages of Their Total 97
17. Maximum Allowable Total Departure for the Five Groups of Accounts 99
18. Percentage Materiality Criteria for the Five Groups of Accounts 100
19. Average Standard Deviations of the Five Groups of Accounts 103
20. Relative Average Standard Deviations of the Five Groups of Accounts 104
21. Percentage Materiality Criteria in a Range Form 106
LIST OF ILLUSTRATIONS
Figure Page
1. Clusters of Seven Hypothetical Variables of Three Factors Extracted From the Illustrative Correlation Matrix Presented in Table 1 67
2. Clusters of Selected Twenty Income Statement Accounts on Two of the Five Principal Factors Extracted From the Empirical Correlation Matrix Presented in Table 5 84
3. Clusters of Selected Twenty Income Statement Accounts on the Five Principal Factors Extracted From the Empirical Correlation Matrix Presented in Table 5 85
4. Cluster of Selected Twenty Income Statement Accounts on Factor 2 of the Five Principal Factors Extracted From the Empirical Correlation Matrix Presented in Table 5 86
Vlll
CHAPTER I
INTRODUCTION
I. General Statement of the Problem
The concept of materiality is of paramount impor
tance in accounting and auditing. Its significance is evi
denced in the authoritative pronouncements of both the Amer
ican Institute of Certified Public Accountants (AICPA) and
the Securities and Exchange Commission (SEC). These pro
nouncements relate to items or events of a material nature.
The concept represents the criterion of determining
whether the pronouncements of the AICPA or the SEC, which
regulate the work of the accountant and the auditor, must be
adhered to in dealing with a particular fact. The state
ments of these regulating institutions concerning recording,
classifying, and disclosing financial facts stipulate that
they apply only to material items. Any departure from the
pronouncements of the AICPA or the SEC should be corrected
or disclosed in notes to financial statements or in the
auditor's report, if the amount involved is material.
Therein lies the paradox. Although the concept of
materiality underlies the pronouncements of the AICPA and
the SEC, the latter have not provided sufficient criteria
for the application of the concept in specific situations.
While the concept may be well-defined on a conceptual basis,
its application presents major difficulties.
A. Definition and Uses of Materiality
Webster's Third New International Dictionary defines
the adjective "material" as:
. . . being of real importance or great consequence: substantial, essential, relevant, pertinent, requiring serious consideration by reason of having a certain or probable bearing on the proper determination of a law case or on the effect of an instrument or on some similar matter.
It defines the word "materiality" as:
. . . the quality or state of being something requiring serious consideration by reason of being either certainly or probably vital to the proper settlement of an issue.
As applied to accounting, Gordon suggests that a
material item is:
. . . a fact, untrue statement or omission of which would be likely to affect the conduct of a reasonable man with reference to the acquisition, holding or disposal of the security in question.
Gordon's definition, however, is a special case connected
with the Securities Act of 1933. In general terms, a
Webster's Third New International Dictionary (Springfield, Massachusetts: G. and C. Merriam Company, Publishers, 1967), p. 1392.
^Ibid. 3 Spencer Gordon, "Accountants and the Securities
Act," The Journal of Accountancy (November, 1933), p. 438.
material fact may be defined as influencing the judgment of
a prudent person such that it makes a difference in making
decisions related to that fact.
Materiality may be applied in two major areas in
accounting. One is concerned with the audit work of deter
mining or estimating the rate of arithmetic or mechanical
error in accounting data. The other is regarding the ac
counting and auditing work related to the technical aspects
of recording, classifying, and disclosing financial facts.
This study is exclusively concerned with the recording,
classifying, and disclosure aspects of accounting and audit
ing work from the technical point of view. Henceforth, the
word materiality will be related only to the recording,
classifying, and disclosure aspects of accounting and audit
ing work, and any departure from the pronouncements and di
rections of the AICPA or the SEC will be referred to as a
departure or deviation from standard accounting practice.
In recording, classifying, and disclosing economic
events and transactions of a business entity, the accountant
is regulated by the pronouncements of the AICPA and the SEC.
The auditor also is regulated by the pronouncements of these
institutions with respect to the planning and execution of
the audit program. The regulating pronouncements are appli
cable only when the item, transaction, account, or departure
from standard practice is material.
At the recording stage, the accountant has to enter
any transaction or event in the books of a particular busi
ness in conformity with generally accepted accounting prin
ciples. Any departure from these principles should be dis
closed in footnotes to financial statements or in the audit
report of the independent auditor. But adherance to these
principles is not required if the item under consideration
is immaterial. If an insurance premium for a three-year
period, for example, is paid in full at the inception of
coverage and recorded in its entirety as an expense, this
treatment would be a departure from standard practice. It
is not recorded in conformity with generally accepted ac
counting principles and must be corrected by recording it as
an asset (unexpired insurance) whose cost must be expensed
over its three years of useful life. But the correction of
this departure will not be necessary if the amount involved
is immaterial.
Unusual nonrecurring gain or loss on sale of a seg
ment of a business, for example, must be classified as an
extraordinary item, segregated from the results of ordinary
business operations, and shown separately in the income state
ment. The classification of such an item as an operating
gain or loss would be a departure from generally accepted
accounting principles that must be corrected or disclosed,
unless the amount of the gain or loss is immaterial.
In order for the financial statements of an entity
to be comparable and more useful to its user, the accountant
must be consistent in applying a particular accounting prin
ciple from period to period. The depreciation method used
by the business, straight-line for example, should be con
sistently followed from period to period. A change to any
other acceptable method should be disclosed. Lack of dis
closure or reference to this change will be a departure
from standard accounting practice unless the effect of the
change is immaterial in the current period and is also ex
pected to be immaterial in its effect in future periods.
Materiality decisions are important to the auditor
in determining the need for, and the extent of, the audit
procedures to be used with respect to a particular item or
event. At the planning stage the auditor uses materiality
as a criterion in determining the items that will receive
limited attention with regard to the exclusiveness of evi
dence gathered or the extent of items examined.
The auditor uses materiality in executing the audit
plan or program when he evaluates departures from standard
accounting practice. The departure that the auditor may
discover here is of the nature given above at the recording,
classification, or disclosure phases. Any departure the
auditor discovers should be corrected or disclosed in notes
to financial statements or in the auditor's report. But
only material departure will require correction or disclo
sure. Additionally, there are other uses of the materiality
concept, such as those concerning disclosures required by
the SEC.
In summary, materiality uses may be classified as
accoxinting uses and auditing uses. In accounting, materi
ality is applied at three stages: the recording, classifi
cation of items on the financial statements, and reporting
on the financial position and the results of operations in
cluding disclosure. Auditors use materiality at both the
planning and the execution phases of the audit program.
Any departure from the pronouncements and requirements of
the AICPA or the SEC concerning these accounting or audit
ing aspects should be corrected or disclosed. The use of
the concept of materiality is to determine whether such a
departure is material enough that it should be corrected or
disclosed. The above discussion illustrates the importance
of the concept of materiality and the need for criteria that
will help the accountant in making his accounting or audit
ing decisions.
B. Judgment Based Materiality
Materiality decisions are generally made on the
basis of judgment. As a result, it is not uncommon in prac
tice to obtain opposite opinions, with respect to materiality,
from two qualified accoiintants under substantially the same
circumstances.
Although many writers and practitioners believe that
materiality is a matter of professional judgment and not
subject to precise quantification, most recommend the use
of some criteria or guidelines to improve the exercise of
this judgment and to provide greater uniformity in its ap
plication.
C. Inadequate Materiality Guidelines
Several criteria have been suggested for improving
the present basis of determining materiality. For example,
in a major study in 1954, approximately 50 per cent of the
respondents to a questionnaire considered relating the amount
of rent expense under long-term lease to average income be
fore taxes as the primary factor influencing their decisions
on materiality. The dividing line between material and im
material departure from standard accounting practice ranged
from 6.6 per cent to 17.6 per cent of average income before
taxes. For other items investigated in the 1954 study,
namely the decline in marketable securities and contingent
4 Sam M. Woolsey, "Judging Materiality in Determining
Requirements for Full Disclosure," The Journal of Accountancy (December, 1954), p. 750.
Carman G. Blough, "Some Suggested Criteria for Determining Materiality," The Journal of Accountancy (April, 1950) , p. 353.
8
liabilities, the respondents indicated different bases of
comparison and different percentages.
A later study, in 1965, suggested the use of the
earning power of the enterprise as the yardstick against
which the materiality of individual items should be measured.
The study was directed mainly to materiality decisions in
auditing. It suggested the use of different percentages of
gross profit, for different profit volumes as a criteria to
be compared with the total amounts of known or possible ac-7
counting departure from standard accounting practice. In
196 7, a third major study dealing with the treatment of ex
traordinary items, revealed that there is no agreed-upon o
criteria for applying the concept of materiality.
Other criteria for determining materiality have been
proposed. Unfortunately, the proposed criteria have been
either limited to a few specific situations, or are of such
a subjective nature that they cannot be used as general guide
lines. The available criteria for measuring materiality are
still deficient in providing a basis for improved judgment g Woolsey, "Judging Materiality in Determining Re
quirements for Full Disclosure," p. 747. 7 Study Group on Audit Techniques, Materiality in
Auditing (Toronto: The Canadian Institute of Chartered Accountants, October, 1965), p. 10.
o Leopold A. Bernstein, "The Concept of Materiality,"
The Accounting Review, XLII (January, 1967), 86.
for accountants and auditors, and more objective and widely
applicable criteria are needed.
II. State of the Art
There are several approaches that interested parties
in accounting have followed in their attempts to solve the
materiality problem. The approaches range from explicit
rigid standards to suggestions merely implying that the ex
istence of some sort of guidelines is necessary for the ap
plication of materiality.
A. AICPA Approach
The American Institute of Certified Public Account
ants (AICPA) has indicated on several occasions that deci
sions concerning materiality should depend on the accountant's
judgment and the surrounding circumstances. Except for a
9 couple of specific cases, it has generally avoided providing any guidelines.
B. SEC Approach
The Securities and Exchange Commission (SEC) has
followed a very different approach from that of the AICPA.
It has provided a clear-cut solution to materiality decisions
9 The Accounting Principles Board of the AICPA gave
one specific materiality guideline about capitalizing a portion of retained earnings for distributing stock dividends in Accounting Research Bulletin No. 43, and another guideline concerning the computation of earnings per share in Opinion No. 15.
10
for some items in terms of a specific percentage or a given
dollar amount. This approach depends on the SEC's authority
and power to prescribe accounting principles and procedures.
Adherence to the SEC pronouncements is obligatory with re
gard to all companies registered with the SEC. It requires
that certain items must be disclosed or shown separately if
they exceed a fixed percentage of a given classification.
A balance sheet account, for example, must be shown separate
ly if it exceeds 5 per cent of total assets or 10 per cent
of the balance sheet caption.
C. Approaches in Accounting Literature
A variety of approaches have been advocated by edu
cators and practitioners in solving the materiality problem.
Some writers have discussed comparing an item to a base stan
dard in order to determine its materiality. Different
bases have been suggested, such as some balance sheet cate
gories, gross income, and net income. Other writers have
emphasized the importance of both the size of the item and
its nature in making their materiality judgments. Still
others have stressed the tools of analyzing financial state
ments, such as ratios or trends, used by investors as guides
U. S. Securities and Exchange Commission, Regulation S-X, Form and Content of Financial Statements (Washing-ton, D. C.: Government Printing Office, 1972) , Rule 5.04.
References and more detailed discussion of this and other writers' approaches mentioned in this section are presented in Section C of Chapter II.
11
to the accountant in making materiality decisions. This
approach of suggesting general guidelines seems to depend
on the experience and judgment of such writers.
Other writers have tried to survey and combine the
experience of a group of accountants, through responses to
questionnaires, to establish some patterns of materiality
decisions concerning a few particular accounts. Still
others have reviewed selected prior decisions of accountants
involving materiality matters to establish similar patterns
of materiality decisions. But again, this approach depends
on others' experience and judgment compared to writers' ex
perience and judgment in the previous approach.
III. Scope of the Study
A. Statement of the Problem
Critical examination of definitions of the concept
of materiality and suggested guidelines for its application
to specific situations, discussed in Chapter II, shows that
there is neither a clear definition of the concept nor any
agreed-upon criteria for making materiality decisions. Un
less materiality decisions are made on an objective basis,
a number of serious problems will continue to be encountered
by the profession. Some of the problems thus engendered
are:
1. Substantial variations and diversity in opinion
and conclusions concerning materiality, even under the same
12
circumstances. Unguided professional judgment ccin be little
12 more than personal judgment.
2. Departure from correct handling of accounts,
following practices that are questionable or even incorrect,
13 a procedure which is likely to discredit the profession.
3. More ambiguity and thereby greater difficulty
for users of financial statements in understanding the na
ture and limitations of accounting information; hence more
divergent and misleading inferences from accounting data.
4. Greater difficulty for the accountant, on whom
the burden of proof to justify his decisions concerning
materiality will always be placed.
5. Difficulty for the staff accountant to under
stand the manner in which materiality is put into practical
effect, especially during the first year or two of his ex-
14 perience.
6. Difficulties in educating and training students
and prospective accountants, created by minimizing the sig
nificance of precision and encouraging inexactitude and ap-
15 proximation in dealing with accounting problems.
12 Delmer P. Hylton, "Some Comments on Materiality,"
The Journal of Accountancy (September, 1961), p. 63. 13 Bernstein, "The Concept of Materiality," p. 92.
14 Ernest L. Hicks, "Some Comments on Materiality,"
The Arthur Young Journal (April, 1958), p. 16. Charles H. Griffin, "Pedagogical Implications of
the Materiality Concept," The Accounting Review (April, 1959), p. 299.
13
7. Undermining confidence in the profession's work
by causing a substantial lack of uniformity and thus hinder
ing comparability which is vital to investment decisions.
B. Nature and Purpose of the Study
The object of this study is to demonstrate a more
objective solution to the materiality problem by utilizing
the capability of the mathematical technique "Factor Anal
ysis" in analyzing the relationships among income statement
accounts. The approach of this study differs from previous
approaches in the basis of establishing the needed criteria
for materiality decisions. The criteria suggested in this
study are based upon statistically analyzing the relation
ships among the accounts that determine net income of the
business. The accounts under analysis may then be grouped
according to their clustering on particular underlying fac
tors that account for the association among the accounts.
This grouping is based on the nature of the accounts and
their interrelationships. Each group of accounts is given
a different weight in establishing the criteria. The weight
or significance of each group is determined by its size as
measured by the sum of its constituent accounts and by its
nature as measured by its contribution to net income of the
business.
1 6 Bernstein, "The Concept of Materiality," p. 81.
14
The underlying assumptions of this study are the
following:
1. The materiality concept does exist in account
ing, and its application presents major difficulties.
2. Net income of the business is of major concern
to all parties interested in accounting information in order
to make decisions related to the business. Therefore, net
income is a convenient basis for measuring the materiality
of the dollar effect of departures from standard accounting
practice. The criteria of determining whether an amount
involved in a deviation from standard accounting practice is
material will be in a percentage form by relating the amount
involved in the deviation to net income of the business.
In other words, net income is used as the basis of compari
son.
3. Some degree of association exists among the
large number of accounts which enter into the determination
of net income.
4. Linear relationships among such accounts and
net income exists on the basis that the more the revenue
the more the net income and the more the expense the less
the net income (other things being equal).
With these assumptions in mind, the purposes of this
study are to:
1. Investigate existing standards and guidelines
with respect to materiality in accounting;
15
2. Collect empirical data concerning income state
ment accounts and statistically analyze their relationships
to obtain a basis for setting guidelines for measuring
materiality;
3. Demonstrate, by using a selected industry,
namely retail trade, the application of factor analysis as
a statistical technique for solving the accountant's materi
ality problem. And depending on the results of the analysis;
4. Devise general guidelines for determining whether
or not X amount in account Y is material, and thus should be
treated according to a specific procedure rather than being
left to the accountant's expediency.
In summary, the objective of this study is to demon
strate the application of "Factor Analysis" as a statistical
technique to solve the accountant's problem of materiality
by providing a more objective criteria for its measurement.
This study intends to establish criteria more ob
jective than those presently existing for applying the con
cept of materiality in accounting. These criteria will have
the potential of:
1. Being a helpful tool for accountants and auditors
in making more objective materiality decisions;
2. Simplifying and saving time and effort spent in
this process of decision making;
3. Providing a degree of uniform and consistent
treatment throughout the profession; and finally
16
4. Promoting consensus among accountants and
readers of financial statements concerning their expected
precision.
IV. Organization of the Study
This study is divided into three parts. The first
part, consisting of Chapters I and II, provides an overview
of the problem of applying the concept of materiality in
accounting and the methodology for solving this problem
through the utilization of the statistical technique of
factor analysis.
The second part (Chapters III and IV) focuses on
the concept and procedures of factor analysis and its ap
plicability to the materiality problem. Chapter III briefly
describes factor analysis and its purpose. The applicabil
ity of factor analysis to solving the problem of material
ity is demonstrated in Chapter IV. The analysis in this
Chapter utilizes as an example the empirical information
collected for this purpose from the retail trade industry.
This Chapter includes the process and the results of devis
ing general criteria for guiding the application of the con
cept of materiality in accounting. The concluding part
(Chapter V) summarizes the analysis, limitations, and con
clusions of the study.
CHAPTER II
METHODOLOGY
The objectives of this study may be divided into two
major parts. The first part is concerned with the investi
gation of existing materiality guidelines. This investiga
tion was accomplished by reviewing the literautre on the
concept of materiality and the bases for its measurement.
The findings are presented in Section I of this chapter.
The second part is concerned with demonstrating the applica
tion of factor analysis to solving the materiality problem
in accounting. The methodology for this part is covered in
Section II of this chapter.
I. Review of the Literature
Discussion of the concept of materiality in account
ing literature is relatively recent. Very little discussion
of the concept is found in pre-World War II literature. At
tention to the concept increased with the development of the
responsibility of the independent accountant for preparing
prospectuses and reports to meet the legal requirements of
the SEC.''"
Warren Reininga, "The Unknown Materiality Concept," The Journal of Accountancy (February, 1968), p. 31.
17
18
From the inception of accounting, materiality has
2 been considered a matter of personal judgment. It has been
defined in many ways. Regulation S-X, Rule 1.02, states
that the term "material," when used to qualify a requirement
for furnishing information as to any subject, limits the in
formation required to those matters about which an average
prudent investor should be informed before purchasing the 3
security registered. The American Accounting Association
in its Accounting and Reporting Standards for Corporate
Financial Statements says:
. . . materiality of an item may depend on its size, its nature, or a combination of both. An item should be regarded as material if there is reason to believe that knowledge of it would influence the decisions of an informed investor. . . . It is a relative matter.
Accounting Research Study No. 7 gives the following defini
tion:
A statement, fact, or item is material, if giving full consideration to the surrounding circumstances, as they exist at the time, it is of such a nature that its disclosure, or the method of treating it, would be likely to influence or to make a difference in the judgment and conduct
2 Paul Frishkoff, "An Empirical Invesigation of the
Concept of Materiality in Accounting," Empirical Research in Accounting: Selected Studies (1970), p. 117.
3 U. S. Securities and Exchange Commission, Regula
tion S-X, Rule 1.02. 4 Executive Committee, Accounting and Reporting Stan
dards for Corporate Financial Statements (Iowa City, Iowa: American Accounting Association, 1957), p. 8.
19
of a reasonable person. The same tests apply to such words as significant, consequential, or important.
Judgment, sound analysis, and experience are the
basic qualities needed to make materiality decisions. Most
definitions refer to a "prudent, reasonable, or informed"
person, and to the influence an item might have upon his
decision. However, these qualities cannot be quantified
and do not provide sufficient guidelines for the implemen
tation of the materiality concept in specific situations.
Many standards and guidelines have been proposed by
individuals, interested groups, and authoritative agencies.
They represent varying approaches to solving the materiality
problem.
A. AICPA Approach
Accounting Research Study No. 7 states:
The fact that no committee of the Institute has defined the terms material, significant, or consequential merely serves to emphasize the fact that the problem involved is largely a matter of judgment to be exercised in the light of all the then-existing surrounding circumstances.
In Opinion No. 9, the Accounting Principles Board
(APB) says:
The segregation in the income statement of the effects of events and transactions which have
Paul Grady, Inventory of Generally Accepted Accounting Principles for Business Enterprises, Accounting Research Study No. 7 (New York: American Institute of Certified Public Accountants, 1965), p. 40.
^Ibid., pp. 38-39.
20
occurred during the current period, which are of an extraordinary nature and whose effects are material requires the exercise of judgment. . . . Accordingly, they will be events and transactions of material effect which would not be expected to recur frequently and which would not be considered as recurring factors in any evaluation of the ordinary operating processes of the business.
The APB then gives some examples of extraordinary items
without defining materiality other than stating that it is
generally a matter of judgment.
The APB, however, gives a specific materiality guide
line concerning the capitalization of a portion of retained
earnings equal to the fair market price of issued stock
dividends if the number of additional shares issued is less
than 20 per cent or 25 per cent of the number of previously
outstanding shares. The distribution of stock dividends
beyond this limit is believed to have a material effect on
the share market price, and hence, the amount of retained
earnings capitalized should equal only the par value of the o
stock issued. Another materiality guideline given by the
AICPA is that concerning earnings per share. In making an ex
ception to using the treasury stock method, the APB considers 7 Accounting Principles Board, Reporting the Results
of Operations, Accounting Principles Board Opinion No. 9 (New York: American Institute of Certified Public Accountants, December, 1966), Paragraph 21.
p Committee on Accounting Procedure, Restatement and
Revision of Accounting Research Bulletins, Accounting Re-search Bulletins No. 43 (New York: American Institute of Certified Public Accountants, June, 1953), Chapter 7, Section B, Paragraphs 10-13.
21
the effect of options and warrants on earnings per share
to be material when they are convertible into a number of
common shares that exceeds 20 per cent of the number of out-
9
standing shares of common stock. This 20 per cent guide
line and the above-mentioned 20 per cent or 25 per cent guide
line apply only to the special situations of earnings per
share discussed in Opinion No. 15 and capitalization of re
tained earnings discussed in Accounting Research Bulletin
No. 43, respectively.
B. SEC Approach
SEC regulations represent fixed standards in deter
mining materiality. They require corporations registered
with the SEC, for example, to file detailed information con
cerning the amount due from their officers, directors or
principal shareholders, if the amount exceeds 1 per cent of
the total assets or if it exceeds $20,000. Other require
ments stipulate that an expense item should be shown sepa
rately if it exceeds 5 per cent of total assets and that op
erating revenue of a subsidiary should be shown if it exceeds
15 per cent of the annual net income. Limits are indicated
also for various other items.
9 Accounting Principles Board, Earnings Per Share,
Accounting Principles Board Opinion No. 15 (New York: ^eri-can Institute of Certified Public Accountants, May, 1969), Paragraphs 36-38.
10, U. S. Securities and Exchange Commission, Regulation S-X, Rule 5.04.
" •"•Ibid., Rule 1.02.
22
C. Approaches in Accounting Literature
A relatively large number of guidelines or standards
for materiality decisions is found in the accounting litera
ture. In answering a question asking for guidance on materi
ality. Carman G. Blough maintained that the Committee on Ac
counting Procedure did not consider it feasible to set down
any general criteria. He personally thought that materiality
should be considered in relation to the net income over a
period of years. In his example of an extraordinary item,
he considered 5 per cent of average net profit immaterial.
He says that the per cent of net income which constitutes
the dividing line between material and immaterial may vary
widely. Some consider 10 per cent to be material, others
20 per cent or 25 per cent. This is in addition to the pos-
12 sible variation of the percentages for different items.
In an attempt to establish a pattern of materiality
decisions in determining the requirements for full disclo
sure, Woolsey conducted a survey of the opinions of differ
ent qualified groups in regard to long-term leases, decline
in the market price of marketable securities, and contingent
liabilities. He found that 64 out of 130 considered "the
ratio of the annual lease payment to average income before
tax" to be the primary factor influencing their decisions on
materiality. The respondents gave, as the dividing line,
12 Blough, "Some Suggested Criteria for Determining Materiality," p. 354.
23
ratios ranging from 6.6 per cent to 17.6 per cent of net
profit before tax. Thirty-two other respondents considered
the number of years remaining in the life of the lease as
13 most important, and gave a range from 2.5 to 17.5 years.
For the second item that Woolsey included in his
study, the decline in the market price of marketable securi
ties, he found that 57 out of 126 considered the ratio of
the amount of decline to the current income before tax as
the most important factor influencing their materiality de
cisions. The ratio that divides between material and im
material ranged between 4.1 per cent and 7.5 per cent of
profit before tax. Twenty-four respondents indicated that
the ratio of the amount of the decline to the cost of the
securities is the most important factor affecting their de
cisions. The average of the ratio given by this group was
14 6.2 per cent of the cost of marketable securities.
Concerning the third item that Woolsey discussed,
contingent liabilities, 37 out of 127 considered the ratio
of the amount of the contingent liability to working capital
as the primary factor in making their materiality decisions.
The suggested ratio ranged from 1.5 per cent to 6.1 per cent
An equal number of respondents considered the actual dollar
13 Woolsey, "Judging Materiality in Determining
Requirements for Full Disclosure," pp. 745-50. 14-rv.- Ibid.
24
amount of the contingent liability as the primary factor
affecting their decisions. Woolsey concluded that there was
some uniformity in the respondents' answers, which suggests
that establishing a centralized bracket for each type of
materiality decision, and using the most important related
15 factor as a base, might be practicable.
Chetkovich said in 1955: "The concept of material
ity should not be used as a refuge for escaping unpleasant
issues but rather a means for separating the important from
16 the unimportant." He maintained that the nature of the
item, as well as its amount, should be considered. Hicks
suggested in 1958 the comparison of cumulative expectable
amounts involved in deviations from standard accounting prac
tice with established minimums in determining materiality.
He identified three classes of items that require quite dif
ferent standards of materiality. The first class includes
items subject to special scrutiny, such as amounts due from
officers or directors, transactions concerning borrowed
money or affecting stockholders' equities, income tax pay
ments, transactions between related companies, and payments
under pension, profit-sharing and similar plans. The second
class of items, requiring different standards of materiality,
consists of items that save money to the enterprise, such
^^Ibid.
16 Michael N. Chetkovich, "Standards of Disclosure,"
The Journal of Accountancy (December, 1955), p. 48.
25
as duplicated payments. And the third class includes situ-
17 ations indicating possible defalcations.
Chan gives two criteria for materiality: the rela
tive size of the item and the nature of the item. Size should
be considered relative to some other pertinent item; for ex
ample, the amount of a specific asset relative to total assets
or an expense relative to sales. The nature of the item,
regardless of the amount, becomes important in cases of such
18 sensitive accounts as amounts due to or from officers.
Hylton says that materiality can be measured on two
bases: a fixed quantity of dollars or a percentage of a
significantly related item. The fixed amoiint of dollars is
irrelevant because it must be changed every time the size
and scope of the business operations change. He believes
that the basis of measurement should not be variable. Since
current net income may vary widely from year to year, he
suggests using gross profit on sales as a more stable basis
by which to measure materiality of income statement accounts.
He suggests, as the dividing line, 2 per cent of gross profit
on sales. For balance-sheet items, he suggests 5 per cent
of a related total or caption in the balance sheet as the
19 standard that separates material and immaterial items.
17 Hicks, "Some Comments on Materiality," p. 11.
" Stephen Chan, "Materiality," The New York Certified Public Accountant, XXXI (June, 1961), 402.
19 Hylton, "Some Comments on Materiality," p. 62.
26
Donald Rappaport in his search in 196 4 for more ob
jective guidelines for materiality decisions surveyed the
users of financial statements and discussed the aims of fi
nancial analysis. He contended that investors represent the
group that depends most heavily on financial information and
their chief interest is to infer the future from the present.
The accountant can use the conclusions that investors might
draw from financial statements as a guide for his materiality
decisions. The conclusions thus drawn are not those of an
average investor, but those interpretations reached after us
ing the best methods of financial analysis. He gave some
qualitative guides for net income, classifications in finan
cial statements, and adequate disclosure of other important
financial information. For example, including or excluding
an extraneous item in current net income depends on whether
the item properly enters in computing average income over a
specific period or earnings trend, or on whether it affects
the measurement of earnings stability. In summary, Rappaport
suggests that judging materiality should depend on whether
an item will affect or distort some financial analytical
tool such as a ratio or a trend that financial analysts use
in making investment decisions after they transform account
ing data into economic indicators.
Bernstein's research study, in 1967, on treating
20 Donald Rappaport, "Materiality," The Journal of
Accountancy (April, 1964), p. 43.
27
extraordinary items, revealed that practice does not appear
to be guided by any discernible standard of materiality.
He found that definite bias exists in showing such extraor
dinary items as special items in the income statement when
they are credits (65 per cent of total credits) and in re
tained earnings when they are debits (77 per cent of total
debits). He believes that judgment is, of course, a vital
part of any professional's work, and if materiality is a
matter of judgment, it should not be mysterious, undefinable,
and inexplicable. Bernstein's study suggested a border zone
of 10 per cent to 15 per cent of a 5-year average of net in
come after tax as the point of distinction between material
and immaterial. But he suggests also that the compound
annual rate of growth on net corporate income (around 5 per
cent) can be deemed significant in many instances and could
21 be used as a guide for materiality.
Reininga emphasizes that materiality should be judged
with respect to its impact, expected consequence, or effect
upon the financial perspective proposed. The effect of the
item on some ratio, working capital, or volume or trend of
profit should be considered in determining materiality and
such ratios or trends are the real standards and guidelines.
He then says:
. . . it is essential that we establish a communication system that will guarantee an exchange of
21 Bernstein, "The Concept of Materiality," p. 86.
28
materiality decisions so that they may be freely discussed, criticized or used as a basis for judgment themselves. Here lies our only hope for the solution of the materiality concept problem.
A more recent study was conducted by Paul Frishkoff
in 19 70. The study was a search for the factors that in
fluence the auditor's opinion on consistency. Frishkoff
examined 2,218 annual reports for this purpose and used the
multiple discriminant technique (a form of regression anal
ysis) in his analysis. He found, at 0.025 level of alpha,
that the absolute effect of the accounting change divided
by net income was the only significant variable that in
fluences materiality decisions of the auditor concerning
consistency. He concluded, at this point, that if the rel
ative income effect is the only factor considered, the
dividing line between material and immaterial would have
been vague, and of little or no predictive value. Using
0.065 level of alpha, and thus introducing additional var
iables, he found that the size of the business (its net
worth) was another factor, and the larger the net worth,
the less the probability of receiving a qualified opin-
23 ion.
22 Reininga, "The Unknown Materiality Concept," p. 32.
Concept of Materiality in Accounting," p. 125.
23 Frishkoff, "An Empirical Investigation of the
29
II. Factor Analysis and Research Design
Demonstrating the application of factor analysis to
solve the materiality problem requires the identification of
all the variables that determine net income. The variables
which are analyzed in this study are income statement ac
counts, and henceforth the words "variables" and "accounts"
will be used interchangeably and refer to the same thing.
The general purpose of factor analysis is to describe
a large number of associated variables by a few underlying,
powerful factors that account for the association among the
variables. An important assumption underlying this study
is that some degree of correlation exists among the accounts
that enter into the determination of net income. This as
sumption indicates that the first step in the analysis is to
measure the degree of correlation between each account and
each one of all other accounts. Whether to include an ac
count in further analysis will be determined by the signifi
cance of its coefficient of correlation with every one of
the other accounts. If the coefficient of correlation of
the account proves to be significant at the 0.95 confidence 25
level, the account will be included in the factor analysis.
O A
Howard L. Balsley, Quantitative Research Methods for Business and Economics (New York: Random House, 1970), p. 256.
25 The T test of significance may be used, and as
applied here, any coefficient of correlation greater than 0.203 will be considered significant. Procedure and discussion are shown in Appendix I.
30
Only associated accounts should be used in the analysis be
cause only associated variables can be reduced to a few
underlying factors. Table 5 in Chapter IV shows that all
variables have at least one correlation coefficient greater
than 0.203 and hence all are included in the analysis. An
underlying factor represents a group of variables clustered
or loaded on that factor.
A. The Factor Model
There are different models that may be used in fac
tor analysis applications. Some models are mathematical
and produce a unique solution, such as the "principal com
ponent" or the "principal axes" technique developed by
Hotelling. The Thurstone model on the other hand is a math
ematical approximation to such models. The Thurstone model
is used in solving an illustrative problem in Chapter III
to give the reader an appreciation of the power of factor
analysis. It is a time-saving alternative to other mathe
matical models, especially when hand-computation is used.
The Thurstone model is used in Chapter III because it is
simple, more easily understood, and produces satisfactory
results. It is usually used when the number of variables
and expected number of underlying factors are relatively
small. It uses the "centroid method" of factor extraction
together with the technique of "rotation of the axes" to
31
26 bring about the simple structure. However, the principal
component method of factor extraction has been used in anal
yzing the empirical data in Chapter IV of this study. The
reason for using this method is the large number of variables
(twenty-five), and the relatively large number of underlying
factors which make the factor extraction and factor rotation
processes laborious. Also, the principal component method
produces a unique and precise solution in contrast with the
approximation solution provided by the Thurstone model.
B. The Variables
27 Twenty-five variables are included in the analysis.
The criterion used for including these variables in the anal
ysis is that the variable must be an income statement account
which is used by retail trade business entities in their
books in computing periodic net income. Therefore, all in
come statement accounts must be included in the analysis.
The twenty-five accounts used in this study have
been selected on the basis of this criterion. Some diffi
culties have been encountered because of the variations in
the details of the classifications of the accounts on one
hand, and the variation in the accounts' titles in different
Balsley, Quantitative Research Methods for Business and Economics, p. 258.
2 7 A list of the twenty-five accounts, their code
numbers, the arithmetic means and the standard deviations of the weights assigned by the ninety-four respondents are shown in Appendix II in the copy of the questionnaire used for this study.
32
entities on the other hand. An effort has been made to make
the number of variables as conclusive as possible.
C. The Data
The data needed concerning these variables are the
actual balances of the accounts at the end of the latest
completed year. The balances of the accounts provide the
information an accountant will need to determine the two as
pects of materiality; namely the size of the account and its
nature reflected by its effect on net income of the business
entity. Converting the account balances to proportional
weights ranging from 0 to 10 has 2 advantages. The first
advantage is that the data are more manageable and more com
parable among different business entities, especially with
respect to size. The second advantage, and of equal impor
tance, is that more responses to the questionnaire asking
for these data can be expected because it will better con
ceal the identity of the responding entities. For these 2
reasons, the questionnaire prepared for collecting the data
seeks weights ranging from 0 to 10 to be assigned to each
of the 25 accounts according to the actual dollar size of
each account. The proportions among the accounts must be
kept and this has been made clear in the questionnaire by
asking respondents to assign a weight of 10 to the largest
account, and a proportional weight to all other accounts
as compared with this largest account.
33
D. The Population
It is repeated here that the purpose of this study
is to demonstrate the applicability of factor analysis to
solving the materiality problem in accounting. The popula
tion to be analyzed for the purpose of this study may be
any type of industry whose members or entities have some
degree of uniformity in their nature and income function.
A high degree of uniformity among the population members
is desirable because the quality of the data collected and
the precision of the materiality criteria based on such data
will depend considercibly on the degree of uniformity. There
fore, this study is limited to only one industry, namely the
retail trade. The population for this research is the com
panies in the retail trade industry that are listed in Fair-
28 child's Financial Manual of Retail Stores (1972). The
number of companies listed in this manual, after eliminating
the foreign companies, subsidiaries, and divisions, is 6 00
companies. Of this number, there are 350 parent companies
and 250 subsidiaries. All 60 0 companies were mailed a copy
of the questionnaire.
E. The Collection and Tabulation of Data
The questionnaire designed to obtain the data needed
was mailed to these 600 companies in the hope that at least
2 8 Fairchild's Financial Manual of Retail Stores (New
York: Book Division Fairchild Publications, Inc., 1972).
34
133 responses would be received to satisfy a 0.95 confidence
29 level or 101 responses for a 0.90 confidence level. The
data received from each respondent consist of twenty-five
weights assigned to the twenty-five accotints listed in the
questionnaire. After receiving the responses, a table with
twenty-five columns has been prepared giving one coded column
to each account. The codes used in the table and the anal
ysis are the serial numbers of the accounts according to
their order in the questionnaire. Coding is helpful for
easier reference to the accounts.
This table of account weights includes the primary
data upon which the factor analysis depends. The first step
in the analysis is to correlate each account, using the
product-moment method, with all other accounts and construct
the correlation matrix which is basic to factor analysis.
Because the communalities are unknown, the diagonal entries
in the correlation matrix are also unknown. The diagonal
of the matrix in the illustrative example of Chapter III is
left blank because these cells will be used in the centroid
30 process of factor extraction. Thurstone writes: "Fortunately, the diagonal entry may be given any value between zero
29 Discussion and computations of determining this
sample size are presented in Appendix III. 30 Balsley, Quantitative Research Methods for Busi-
ness and Economics, p. 260.
35
31 and unity without affecting the results markedly, . . . "
However, in order for the analysis to account for the com
plete variance of all the data, unity is entered in the di-
32 agonal cells of the correlation matrix.
F. The Number of Factors
Factoring the correlation matrix usually stops at
the point where no additional significamt variance remains
in the residual matrix. The point of stopping further fac
toring depends on the judgment of the researcher in deciding
whether the residual variance is near zero.
Rotation of the extracted factors may distort the
results of analysis if inadequate attention is given to de
termining the best number of factors. This is because the
loading and interpretation of rotated factors may differ for
the same data. Therefore, the selection of the best number
of factors is highly important.
For some factor analysis models, such as alpha factor
analysis, there is no problem concerning the best number of
factors because it is determined mathematically. But other
models, like the Thurstone model and the principal component,
do not have specific solutions to this problem. Only general
•3 1
L. L. Thurstone, The Vectors of Mind (Chicago: The University of Chicago Press, 1940), p. 108.
32 B. Fruchter, Introduction to Factor Analysis (Prince
ton, New Jersey: D. Van Nostrand Company, Inc., 1954), p. 99.
36
subjective criteria has been developed to give general aid
to researchers.
The eigenvalue-one criterion is one of the general
popular guides to selecting the best number of factors. It
requires limiting the factors to those with eigenvalues
greater than unity. This criterion, however, should be used
with caution, especially in the case of factors with eigen
values close to xinity. Consider, for example, a factor hav
ing an eigenvalue of 1.02 and the subsequent factor having
one of 0.96. It appears hardly meaningful to include one
33 and drop the other. Keeping this precaution in mind, this
criterion is used in determining the best number of factors
in Chapter IV of this study because of its simplicity and
satisfactory results.
G. The Rotation of the Axes
Factor rotation may be analytical or graphical.
Graphical rotation is a visual approach. It consists of
plotting variables' loadings on each pair of factors on
Cartesian coordinates and then visually rotating the axes
around the origin to bring about the simplest structure
which defines better the clusters of the variables on par
ticular factors. There are two graphical rotations: the
orthogonal rotation, which is an approximation to the simple
structure, and the oblique rotation, which is more precise
33 R. J. Rummel, Applied Factor Analysis (Evanston:
Northwestern University Press, 1970), p. 362.
37
and provides a clearer picture of the relationships among
the factors. Orthogonal rotation defines only uncorrelated
factors, but oblique rotation is more flexible and defines
34 factors regardless of their correlation. The analytic or
algebraic rotation is used when the number of extracted fac
tors is large because the graphical rotation becomes labor
ious.
For the purpose of this study, the graphical rota
tion has been used in the illustrative example in Chapter
III. But since the number of factors involved in the em
pirical analysis, in Chapter IV, is expected to be greater
than three factors, two algebraic methods of rotation have
been used: the varimcix orthogonal rotation and the oblique
rotation. The results of the two methods of rotation will
be used in clustering the variables in Chapter IV. Rotated
factors are then explained according to the nature of the
variables clustered on each factor. This explanation may
be useful for more understandable communication and general
ization.
These few underlying rotated and explained factors
are used as a basis for establishing criteria for measuring
materiality. The purpose of using factor analysis in this
study is to cluster or group the accounts on the basis of
the intercorrelation among them. The significance or mater
iality of each group is determined according to the absolute
" Ibid., p. 147.
38
total of the accounts in the group and the contribution of
the group to net income.
As materiality depends on both the size and the na
ture of the item, the procedure followed here emphasizes
both of these aspects. As perceived here, the nature of the
item implies its direct effect on net income, which is a ma
jor concern of all parties. Therefore, both the absolute
size of an item and its direct effect are considered in es
tablishing the criteria of measuring materiality.
III. The Criteria Based on Factor Analysis
Following factor analysis which provides the clusters
or groups of accounts, the identified groups are used as the
basis of setting the criteria for materiality as follows:
1. According to the nature of every account in a
group (a revenue or an expense) and its positive or negative
effect on net income, the contribution of the group to net
-4
in -I
n
income is computed by adding revenues and profits of the j
given group on one side, and then subtracting the expense ^
and loss accounts of that group. The purpose of this step
is to compute the contribution of each group of accounts to
the final results of operations (net income) of the enter
prise. The contribution of a group to net income is a meas
ure of one aspect of its significance.
2. The absolute sum of the accounts in each deter
mined group is computed in order to incorporate the size of
39
the items involved in the establishment of the criteria.
This cdssolute total is the measure of the second aspect of
the importance of the group. It recognizes the materiality
of the group by giving consideration to its size. So,
revenue figures are added to expense figures in the group
to get the overall size of the accounts mixed in given pro
portions to produce the contribution to net income deter
mined in paragraph 1 above.
3. Since the study is concerned with the effect on
net income of the deviation of an item from standard account
ing practice, equal weight must be given to amounts of spe
cific accounts having equal effect on net income. In order
to assign such equal weights, the net contribution of each
group is reduced to one unit of income by dividing both the
absolute total of the group and its net contribution to in
come (which could be negative or positive contribution) by
the net income it contributed. This gives the amount of
money (or weights as the case is in this study) in the given
group of accounts and of its specific mix that contributes
one dollar (or one weight) to net income, and thus has a
significance equal to any other amount from any other group
that contributes one unit to net income.
To illustrate the computations, assume that a given
number of accounts are clustered into two groups. Group I
is assumed to have an absolute total of $1,000,000 and con
tributes $200,000 to net income. Group II has an absolute
40
total of $2,100,000 and contributes $300,000 to net income.
By dividing the absolute total and the contribution of Group
I by $200,000 (its contribution to net income), the $5.00
combination of accounts is this group produces $1.00 of net
income. The same result may be obtained by multiplying both
figures (total and contribution) by the reciprocal of the
income contribution of Group I (1/200,000). The application
of this equalization process to Group II indicates that
$7.00 combination or mix of accounts in this group contri
butes $1.00 of net income, equal to the contribution of
$5.00 in Group I.
It is worthwhile at this point to note that a posi
tive or negative contribution of $1.00 to net income should
be treated as having the same degree of importance to the
person interested in net income of the business, regardless
of the fact that a positive contribution is favorable while
a negative contribution is not. This is because if a dollar
more net income is important and will cause the investor,
for example, to act favorably, a dollar less net income will
cause a different action.
4. For greater convenience in later computations,
and to keep the groups' importance in the same order and pro
portion, the fractions of the groups (the multiples of abso
lute size and net income contribution of the groups to equal
ize their effects in paragraph 3 above, 1/200,000 and
41
1/300,000) are converted to percentage terms. So, putting
1/200,000 4- 1/300,000 = 100%, the fraction of Group I (60%)
gives equal contribution to net income as (40%) of Group II.
These percentages are then used, in paragraph 6 below, to
allocate the portion of net income considered to be material
among the determined groups.
5. The portion of net income that is considered to
be the dividing line between material and immaterial depar
ture from standard accounting practice in the accounts, and
thus requiring a different accounting or auditing decision,
is 5.92 per cent. This ratio represents the average of the
35 E/P ratio for a random sample of 133 companies in the retail trade industry. It is the reciprocal of the P/E ratio m{
m which is widely used by financial analysts. It has been ^
computed by: -I
(a) Dividing the earnings per common share .-.
for the latest year (1972) by the arithmetic mean
of the reported market price per common share ( (high
+ low) divided by 2) to obtain the E/P ratio for
each company, then
(b) Computing the arithmetic mean of the 133
E/P ratios computed in step (a) above.
This E/P ratio, which represents the earnings per
dollar of the stock selling price, is used as the basis for
Discussion and computations of this sample size are shown in Appendix III.
42
determining the portion of net income that divides material
and immaterial total dollar effect of departures from stan
dard accounting practice. The reason for using this E/P
ratio is that it is based on two current dollar value fig
ures (the earnings per share and the share market price).
In contrast with other available financial ratios, the ra
tio of these two current values will be more valid and
closer to what may be called the actual or effective rate
of return on investment. In the earnings-to-net-worth ra
tio, for example, net income is compared with common stock
holders' equity or net worth which means comparing current
dollar value figure (net income) with historical value
figure (net worth). H
Another reason for using the E/P ratio is that it ; !!
considers the current amount of investment (one dollar of -i
share market price) that produced the given amount of net
income. This characteristic is lacking in the earnings-to-
net-sales ratio which compares net income with net sales
without giving any consideration to the amount of invest
ment that produced the net sales or net income. It is used
also because it is one of the major factors upon which the
investor depends in making his investment decisions. It is
important to the investor or any analyst of the business
because it gives in the most concise form an important indi
cator to the investor (or other persons interested in net
43
income of the business) about the profitability of the busi
ness, and enables him to compare different opportunities to
make a decision.
Therefore, the E/P ratio (5.92%) should be consid
ered as consequential and influential on the judgment of
the business analyst in making his decisions. If 5.92 cents
of one dollar of investment are considered to be material or
significant to the investor in making an investment decision,
by the same token, 5.92 cents of one dollar of net income
should equivalently be material and should make a difference
in any judgment related to net income. Relating this ratio
to the materiality problem and the dollar effect of depar
tures from standard accounting practice, it may be said that -i
total dollar effect of departures of 5.92 cents of one dol
lar of reported net income should be the maximum allowable ' >
departure from standard accounting practice in the books.
Any dollar effect of departures accumulating from different
sources and accounts that amounts to 5.92 per cent of reported
net income of a business should be considered material and be
corrected or disclosed. In other words, 5.92 per cent of
business net income in the retail trade industry should be
the dividing line between material and immaterial total dol
lar effect of departures from standard accounting practice
known or discovered in the books.
6. If the average net income of the retail trade in
dustry, which will be estimated in this study, is assumed to
44
be $500,000 (the sum of the $200,000 contribution of Group
I and the $300,000 contribution of Group II given in para
graph 3 above) and using the proportions of the example
computed in paragraph 4 above (60 per cent of Group I gives
equal contribution to net income as 40 per cent of Group II),
the materiality criteria for each group will be determined
as follows:
(a) The portion of net income which consti
tutes the dividing line between material and imma
terial total dollar effect of departure from stan
dard accounting practice is computed by multiply
ing net income ($500,000) by the significant ratio
5.92 per cent, and this gives $29,600 ($500,000 x . m
5.92% = $29,600). This means that if the total X
dollar effect of departure from standard practice . u
in the accounts of a business is equal to or greater r*
than $29,6 00, it will be considered material.
(b) This maximum total ($29,600) is allocated jj
between the two groups of accounts according to C
their significance as measured by the proportion
of the group that gives equal contribution to net
income (60 per cent of Group I and 40 per cent of
Group II). This allocation provides the maximum
allowable total dollar effect of departure from
standard accounting practice in each group. Total
dollar effect of departures in Group I, for example,
45
should not equal or exceed $17,760 ($29,600 x
0.60 = $17,760), otherwise, it should be corrected
or disclosed. Group II total dollar effect is com
puted in the same way and equals $11,840 ($29,600
x 0.40 = 11,840).
(c) In order to enable its use for individual
accounts in each group, the maximum total dollar
effect in each group is transformed into a percent
age form relative to the absolute total of each
group (computed in step 2 above and assumed to be
$1,000,000 for Group I and $2,100,000 for Group II).
This percentage will be the criteria of materiality
for each group. The percentage criteria for Group
I will be 1.8 per cent ($17,760 - $1,000,000 = Jj to
0.01776 or 1.8%) and 0.56 per cent for Group II j
($11,840 T $2,100,000 = 0.00564 or 0.56%). The per- J
centage criteria for one group will be the materi- f 1 li
ality criteria for each of the accounts in this jj
group. Therefore, any departure in account X of '**
Group I that equals or exceeds 1.8 per cent of this
account should be considered material and thus be
corrected or disclosed.
From the dispersion of the weights assigned by the
respondents for the accounts in each group, as measured by
the standard deviation of each account and discussed later
in Chapter IV, a probabilistic range of the percentage
-I
46
criteria could be computed as follows:
(a) Find the arithmetic mean of the standard
deviation of the accounts included in each group
(assume that this arithmetic mean equals $2,000
for Group I accounts which is assumed to have an
absolute total of $1,000,000 in paragraph 3 above).
(b) Transform this arithmetic mean ($2,000)
into a percentage form relative to the absolute size
of this group ($1,000,000). This provides 0.2 per
cent ($2,000 v $1,000,000 = 0.002 or 0.2%) which
represents the standard deviation in this group put
in a percentage form in order to construct the con
fidence interval of the materiality criteria for ^ m
this group. j^
(c) Using 0.90 confidence level, for example, ,.,|
(1.645 standard deviates on each side of the arith- f*
metic-mean-based criteria) will give the following !,
confidence interval for the materiality criteria of J»
Group I:
1.8% ± 1.645 (0.2%)
= 1.8% ± 0.329%
= 2.13% , 1.47%
The 0.90 confidence level used here means that 90
times out of 100 the materiality criterion based on the uni
verse arithmetic means of the accounts involved in Group I
will fall within the interval 1.8% ± 1.645 (0.2%); where the
47
1.8 per cent is the materiality criterion based on the arith
metic sample means of the accounts involved in Group I and
0.2 per cent is the arithmetic mean of estimated standard
deviations of the universe from which the accounts involved
in this group were drawn. The range of percentage criteria
will allow the use of professional judgment, within the
determined limits, in making materiality decisions under dif
ferent circumstances.
Under normal circumstances and concerning accounts
involved in Group I, the accountant may use the mean cri
terion 1.8 per cent as the maximum allowable total dollar
effect of departures from standard practice in any account
of this group. If the inventory account balance (one of the "I
accounts in Group I) in the books is $100,000 and the auditor T-"
was not able to observe taking physical inventory of a j^j rj
$1,600 portion of it because he was late, he may use the
mean criterion (1.8 per cent which produces a maximum limit
of $1,800 of departure from standard practice) and conclude
that not observing $1,600 inventory is immaterial. But if
there are any doubts concerning the existence of the $1,600
inventory, the auditor may use the lower limit of the criter
ion (1.47 per cent which limits the dollar effect of the
departure from standard practice to a maximum of $1,470) and
conclude that this amount is material and should be mentioned
in his report as a qualification to his opinion. However,
for inventories where the possibility of its nonexistence is
48
quite remote, the auditor may use the upper limit of the
criterion (2.13 per cent which produces a maximum of $2,130)
and consider not observing a $2,000 portion of the inventor
ies as immaterial and need not be mentioned in his report.
IV. Summary
In summary, the review of the literature indicates
the existence of a number of approaches to solve the problem
of applying the concept of materiality to specific situations.
These approaches range from avoiding the problem and leaving
it entirely to the judgment of the accountant (AICPA), to
prescribing strict standards (SEC). None of the suggested
solutions, however, gives general, widely applicable, or ob-"1
jectively based guidelines. Most of the proposed criteria ppl >t
are based on judgment. The approach of this study is based j/) -I
on analyzing the relationships among the accounts by utiliz- ftl ing the statistical technique "factor analysis." Using this
n »"• ••. •
r '
technique helps establishing an objective basis for group- i'i
ing the accounts in order to devise materiality criteria ;;U
that incorporates the size and the nature aspects of mater
iality of each group of accounts.
The suggested technique discussed in this chapter
consists of two stages. The first stage is the factor an
alysis of the data collected on income statement accounts
in order to cluster the accounts into groups of materiality.
The second stage is to use the groups resulting from factor
analysis to determine the materiality criteria for each
49
group depending on its size and contribution to net income.
Then, a confidence interval for the criteria is suggested
to be established to allow the exercise of professional
judgment in applying the criteria with a degree of flexibil
ity to fit varying existing circumstances.
The technique discussed in this chapter will be
applied to the analysis of the empirical data on income state
ment accounts in order to demonstrate the establishment of
materiality criteria for the retail trade industry in Chap
ter IV. This will follow the discussion of the concept and
techniques of factor analysis introduced next in Chapter
III.
-I
-I
a ••' •
I ->
<
CHAPTER III
FACTOR ANALYSIS
I. Introduction
The purpose of this chapter is to discuss factor
analysis as a statistical technique and its applicability
to the materiality problem in accounting. Factor analysis
is a multivariate statistical technique. It is concerned
with the analysis of a relatively large number of variables
for the purpose of seeking out a few underlying basic fac
tors that account for the association among the variables. -I
It IS an attempt to show, in quantitative terms, the pat- m 1 T>
tern of relationships among the variables. The few emerg- LO •H
ing underlying factors are a concise embodiment of the asso- ''
elation among the data and can be used in place of the large
number of variables. Thus, the principal objective of fac- [ ^'
tor analysis, as expressed by Harman, is: " . . . to attain J' 2
scientific parsimony or economy of description."
This definition implies a basic assumption in factor
analysis. This basic assumption is that the variables in the C. J. Adcock, Factorial Analysis for Nonmathemati-cians (Melborne: Melborne University Press, 1954), p. 9.
2 Harry H. Harman, Modern Factor Analysis (Chicago:
The University of Chicago Press, 1967), p. Z\ 50
51
problem must have a degree of association among them. As
sociation may best be described by correlation, such as
Pearson's product-moment correlation, and Kendall's or
Spearman's rank correlation. Correlations are computed be
tween each variable and all other variables and then placed
in a square correlation matrix, with the names of the vari
ables shown on each axis, in order to be factor analyzed.
Another assumption frequently made in factor analysis is
that of linearity of the model for simplicity purposes.
The assumptions made in this study, as presented in
Chapter II, are consistent with the two assumptions of fac
tor analysis just mentioned. It has been assumed that some
degree of association exists among the variables, and that . m
the relationships among the variables are linear. >< •Ji
As applied to the materiality problem in accounting, .
this study analyzes the intercorrelations among twenty-five <
selected accounts which are used in determining net income
of a business. Net income is assumed here to be of major
concern to all parties interested in accounting information.
The materiality of any departure from standard accounting
practice in the accounts of the business is measured by re
lating the amount involved to the business net income.
The purpose of analyzing these twenty-five selected
accounts is to seek the basic underlying factors that account
for the intercorrelations among them. The underlying factors
thus emerging will represent all the twenty-five accounts.
52
each factor representing a number of accounts. These fac
tors, or groups of accounts, will be identified and used as
a basis for solving the materiality problem. The solution
will be in terms of criteria against which the materiality of
any departure from standard accounting practice will be
measured.
II. Importance of Variations in the Data
Although any matrix, not necessarily a correlation
matrix, can be factored, it is important to know that not all
matrices will yield factors that may scientifically be useful.
The value of factor analysis depends on the existence of 3
meaningful variability in the data. That is, if the data -4
have no variation, or if the values of a given variable are m >>C
the same among all the businesses or subjects involved in the y} -I
study, no more than one factor can be derived from the data. rl Meaningful variation can be shown and satisfied by
noting patterns in the relationships among the variables, J J
the existence of an underlying order, or causal uniformi- »I3
ties. This variation is related to the matrix of raw data
which shows tlie variables that will be analyzed at the top
(that is, horizontal axis) and the subjects of companies
studied to the left (that is, vertical axis) of the matrix.
Variability in the data may be in the columns of the matrix,
that is, the value of a given characteristic differs or varies
•rk
3 Rummel, Applied Factor Analysis, p. 13.
53
in the population from one member to another, or in the rows
where the values of different characteristics vary from one
characteristic to the other for the same member of the pop
ulation.
The data concerning the twenty-five variables in
this study are assumed to have this important quality of
variation because of the differing proportions of the vari
ables in the same business. In other words, it is expected
that the values of variables in a particular business will
be different—the amount of depreciation expenses differing
from the amount of tax expenses or rent expenses. Variation
is also expected in the value of a given variable, such as
payroll expense, from one company to the other for a large
number of causes, e.g., size, nature of the business, man- >i
agement policy, and degree of automation.
III. Uses of Factor Analysis
Factor analysis may be used for several purposes.
It can be used, for example, as a data reduction technique to
simplify and reduce a multivariate problem to a smaller set
of dimensions in order to enable the researcher to utilize
data on a large number of variables. It is also used as a
clustering technique to enable the researcher to classify a 4
variety of observations into a small number of clusters.
Factor analysis is used here for the purpose of classifying
Jagdish N. Sheth, "Using Factor Analysis to Estimate Parameters," American Statistical Association Journal, LXIV (September, 1969), 808.
54
the twenty-five income statement accounts into a smaller set
of clusters in order to use these clusters as a basis for
establishing materiality criteria.
IV. Criticism of Factor Analysis
Factor analysis has been criticized on several
grounds. One of these criticisms is based on the misconcep
tion that the data must have multinormal frequency distri
bution or at least must be measured on an interval scale.
But such a distribution is required only when tests of sta
tistical significance are applied to the factor results, not
to the data to be factor analyzed.
Another criticism states that factor analysis as
sumes additivity and linearity in the data. These assump
tions are not necessary, and the factors themselves may in
volve complex functions that are nonadditive or nonlinear.
When such assumptions are made, they are usually made just
for convenience and simplicity.
Factor analysis has also been criticized as being
arbitrary in the sense that different researchers may arrive
at different answers using the same data and technique. But
a complete factor analysis of a data matrix is mathematically
unique. Arbitrariness may be partly involved in rotating
manually the factors after the factor analysis is completed.
5
Ibid.
Rummel, Applied Factor Analysis, p. 17.
6
55
Mathematical solutions of the rotation problem through com
puters, however, has decreased the degree of arbitrariness
considerably. The only possible arbitrariness lies in the
research design decisions.
V. Models of Factor Analysis
A variety of factor models may be used to analyze
the correlations among the variables under consideration.
The Thurstone model is a simple one and produces satisfac-o
tory results. It uses the centroid method of factor ex
traction which is a mathematical approximation to the more
mathematically involved and computationally laborious prin
cipal axes or component method developed by Hotelling. The HI
centroid and the principal aixes methods are group or multi- rtf
pie-factor analysis approaches. By utilizing either one of f/J
these methods, any number of factors can be extracted con- r!^
^Ibid., pp. 17-19. p Balsley, Quantitative Research Methods for Business
secutively from the intercorrelation matrix. This extrac-i; -
tion process stops at the point where the residual intercor- f.>
relation variance approaches zero. The relationships among -ij
the extracted factors may then be refined to what Thurstone
calls a "simple structure" by the technique of the "rotation
of the axes" which helps determine the clusters of the vari
ables .
and Economics, p. 258.
56
VI. Correlation Matrix
Adcock states that "the basis of factor analysis is
that if two activities involve a common element there will 9
be a correlation between them." A correlation coefficient
is a measure of the degree of association among variables.
Its value ranges from +1, indicating perfect positive corre
lation, to -1, indicating perfect negative correlation, while
complete lack of correlation is indicated by zero.
The correlation coefficients in the correlation matrix
express the degree of association between the column and row
variables of the matrix. This means that a particular cell
value in the intercorrelation matrix expresses the degree
of association between the column variable which intersects ,»l
the corresponding row variable at this cell. The correla- 5" ih
tion matrix is constructed after collecting the data on all ,.,|
variables involved in the study. Each variable is correlated ^
with all other variables and resulting correlations are ar
ranged in a matrix form with names of the variables on both
axes. It is obvious that the resulting matrix will be square
because the variables heading the columns of the matrix are
the same variables placed to the left of the rows. The
twenty-five columns of income statement accounts, in the
correlation matrix in this study, have twenty-five corres
ponding rows.
p. 19. Adcock, Factorial Analysis for Nonmathematicians,
57
The diagonal of a correlation matrix represents the
correlation of a variable with itself, and this coefficient
must equal 1. The entries in this diagonal may be given any
value between zero and unity. It has been left blank in the
illustrative example in this chapter because the diagonal
blank cells will be used in the centroid process of factor
extraction. In analyzing the empirical data of this study,
however, unity is entered in each diagonal cell because the
principal component method of factor extraction is used.
Unity is entered in the principal diagonal whenever the
study needs to account for all the variance in the data.''"'
Table 1 below shows a correlation matrix of a hypo
thetical example used to discuss, in the following paragraphs,
the procedures and techniques involved in the Thurstone
model. It shows the correlations among seven variables iden
tified by the numbers 1, 2, 3, . . . 7 . One would notice
that the correlations below the blank diagonal are the same
as those above it. This is true because the correlation be
tween any two variables is identical with the reversed cor
relation, i.e., the correlation between the variables 1 and
2 (0.97) is the same correlation between variables 2 and 1
just reordered.
Balsley, Quantitative Research Methods for Business and Economics, p. 260.
11
-I
Fruchter, Introduction to Factor Analysis, p. 99.
58
TABLE 1
ILLUSTRATIVE CORRELATION MATRIX OF SEVEN HYPOTHETICAL VARIABLES
Variables
1
2
3
4
5
6
7
1
0.97
0. 96
0. 70
0. 78
0.40
0.48
2
0. 97
0. 94
0.68
0. 70
0. 52
0. 50
VII. Centroid
3
0.96
0. 94
0. 74
0. 64
0.47
0. 54
Method
4
0. 70
0.68
0. 74
0. 90
0.62
0. 58
5
0. 78
0. 70
0.64
0.90
0.50
0. 52
6
0.40
0. 52
0.47
0.62
0. 50
0. 92
of Factor Extraction
7
0.4 8
0. 50
0. 54
0. 58
0. 52
0.92
The centroid method is a mathematical technique used
to extract consecutively, from the correlation matrix, one 3
factor after the other. This method is a mathematical ap- SJJ
proximation to other more mathematically involved methods of ""J
factor extraction. After placing the correlation coeffi- ,r2
cients in a square matrix, like that of Table 1, with the j •J
variables' names on both axes, the centroid method may be ,!.!
used to extract the factors that account for the intercor
relations among the variables. Each extracted factor is
placed in a table of factor loadings with a column of the
names of the variables to the left of the extracted factors.
Extracted factors are numbered according to the sequence of
their extraction.
After each factor is extracted, the residual matrix
of correlation is computed to determine whether the total
59
residual correlation variance approaches zero. A residual
matrix is computed by first reproducing the variances re
moved in extracting the preceding factor. Reproduction of
variances is done by using the factor loadings just calcu
lated in the latest factor extraction. Reproduced variances
are then subtracted from the preceding correlation matrix
in order to obtain the residual matrix that may be used for
further factor extraction. If residual correlation variances,
in the analyst's judgment, are not near zero, the centroid
method will be repeated to extract one more factor, until
the residual correlation variances are reduced to near zero.
When residual total variance approaches zero, this means
that approximately all the variance represented by the cor- -I
relations has been removed, and that extracted factors ac- jv
count for all the variance that has been removed through the -i 'I
factor extraction process.
Table 2, on the next page, shows the unrotated cen
troid factors that have been extracted, by using the centroid
method, from the intercorrelations in Table 1. Columns 2,
4, and 6 define the extracted factors, and the rows refer to
the variables analyzed. The intersection of a given row and
column gives the loading of the row variable on the column
extracted factor. The table shows three factors which may be
thought of as three different kinds of influences on the
data, or as three categories by which the data may be clas
sified. The loadings of the variables measure the degree to
60
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61
which the variables are involved in the factors. Squared
loading gives the per cent of variation in a variable ac
counted for by each one of the extracted factors. 2
The h column to the right of the table shows the
communalities or the proportion of variance of each variable
represented by the extracted factors. It is simply the sum 2
of squared loadings of each variable. The h corresponding
to variable 7, for example, equals 0.9 321. It is obtained
by squaring its loadings on the three extracted factors 2 2 2
(0.76 , -0.59 , and 0.08 ) and summing these squared load
ings (0.5776 + 0.3481 + 0.0064 = 0.9321). It means that
more than 93 per cent of the variance of variable 7 is ac-2
counted for by the three factors. The average of h column ni
gives the per cent of total variation in the data accounted >(t ;/)
for by the three extracted factors. VI
The total of the squared loadings column of each "» *
factor is called the eigenvalues of that factor and gives j
the amount of variation in the data accounted for by the /
factor. The arithmetic mean of the eigenvalues of a factor '<
represents the per cent of total variance in the data ac
counted for by the factor, i.e., it measures the strength 12 or comprehensiveness of the factor. Factor 1, for example,
accounts for 0.71 of the total variance. Factor 2 for 0.15, and Factor 3 accounts for only 0.075 of the total variance
12 Rummel, Applied Factor Analysis, p. 137.
62
in the data. This indicates that the amount of variation
in the data described by each factor decreases successively
with each factor, and that Factor 1 represents the strongest
or most general pattern of relationships in the data, and
Factor 3 delineates the weakest factor.
The principal axes method of factor extraction, in
contrast with the centroid, has the advantage of providing
a unique solution. Each factor extracted accounts for more
of the variance in the data than the succeeding factor and
13 leaves minimum residuals. In order for the analyst to get
the minimum number of factors, the principal component method
14 should be used in extracting the factors. The original
data may be represented by a smaller number of factors, and ^}
the same amount of variance to be removed from the data will
require a smaller number of factors than that required if
the centroid method is used.
The factor extraction process, using the principal
component method, is essentially the same as that of the cen
troid with respect to using first factor loadings in comput
ing the first residual matrix to be used in extracting the
second factor loadings, and so on, until the residual cor
relation variance approaches zero. The only major difference
•'•"L. L. Thurstone, Multiple-Factor Analysis (Chicago: University of Chicago Press, 1947), pp. 176-79.
"^^Fruchter, Introduction to Factor Analysis, p. 99.
63
in the computations is that the calculation of the first
factor loadings is based upon the first eigenvalue and eigen
vector determined through an iterative process."^^
VIII. Rotation of the Axes
The purpose of rotating the axes is to obtain the
simplest picture that reveals the nature of the relationships
between each pair of extracted factors and makes the identi
fication of the factors easier. It is necessary because
the clustering or the loadings of the variables on each fac
tor is usually not clear and does not give adequate informa
tion for determining what variables are more highly loaded
on a particular factor.
Rotation of the axes, as mentioned earlier in Chap
ter II, may be analytical or graphical. Analytic rotation
is an algebraic approach which is preferred when the number
of expected factors is large. Graphical rotation, on the
other hand, may be used when the expected number of factors
is small as is the case in the illustrative example in this
chapter. Since the expected number of underlying factors in
this study is relatively large, the analytic rotation is used
in analyzing the empirical data in Chapter IV. The algebraic
solution of both, the varimax orthogonal rotation and the
Fruchter, Introduction to Factor Analysis, gives a brief listing of the steps involved in Chapter VI.
Balsley, Quantitative Research Methods for Business and Economics, p. 268.
64
oblique rotation, are given in the analysis in Chapter IV.
Rotation, whether graphic or analytic, may be orthogonal or
oblique. Oblique rotation is preferred because it gives
more precise and distinct clusters of the variables on the
factors. It is more flexible than the orthogonal rotation
because it does not assume that factors are not related to
each other (orthogonal or uncorrelated). The varimax rota
tion, on the other hand, is generally accepted as the best
17 analytic orthogonal rotation. It comes closest to the
Thurstone simple structure. It involves maximizing the vari
ance of squared factor loadings on a pair of factors at a
time by increasing the number of high and low loadings on
18 each factor. _, •I iti
Oblique rotation is done by plotting the loadings of !*f
two factors at a time on cartesian coordinates and rotating „l
the axes in a way that changes the positions of the factors "5
with respect to the axes, keeping their original relation-J
ships constant. More specifically, the rotation of the axes J
intends to reach a simple structure by rotating the axes '
". . . in such a way as to increase the number of zero load-19 ings and decrease the number of negative loadings." In
order to keep the relationships among factor loadings constant.
1 7 Harman, Modern Factor Analysis, p. 311; and Rummel,
Applied Factor Analysis, p. 390. 1 8 Rummel, Applied Factor Analysis, pp. 390-93.
48.
19 Adcock, Factorial Analysis for Nonmathematicians,
65
a normalizing process is used in computing the rotated fac
tor loadings. The results of rotating the factor loadings
of Table 2 are shown in Table 3 below.
TABLE 3
OBLIQUELY ROTATED THREE CENTROID FACTOR LOADINGS EXTRACTED FROM THE ILLUS
TRATIVE CORRELATION MATRIX PRESENTED IN TABLE 1
Variables
1
2
3
4
5
6
7
Factor 1
0.00
0.14
0.13
0.28
0.20
0.85
0.85
Factor 2
0.89
0.78
0. 78
0.63
0.67
0.00
0. 02
Factor 3
0.51
0.54
0. 56
0.02
0.00
0.34
0.45
The results may also be presented graphically in order to
of three dimensions or factors. If the results that need to
be presented graphically involve more than three factors, a
selection of two or three factors has to be made, or several
20 pairs of factors have to be graphed.
The clustering, for example, is obvious in the case
of Factor 1, in the table, where the loadings of variables 6
h -I
show more clearly the clusters of the variables. This graph- j
ical presentation of factor results is limited by a maximum »
20 Rummel, Applied Factor Analysis, p. 484.
66
and 7 are very high on Factor 1, while their loadings on
Factors 2 and 3 are very low. This means that variables 6
and 7 are exclusively clustered or involved in Factor 1. But
the clustering of variables 1 through 5 on Factors 2 and 3
is not equally clear because all the five variables are highly
loaded on Factor 2, while only two of the five variables are
loaded very low on Factor 3 (variables 4 and 5). In other
words, variables 1 through 3 are loaded on and involved in
the two factors, 2 and 3. Figure 1 on the next page shows
the clustering more clearly. The loadings of the seven var
iables on these two factors, 2 and 3, are plotted on carte
sian coordinates, with Factor 2 assigned to the horizontal
axis and Factor 3 to the vertical axis, and the variables'
numbers designated to the intersection of its corresponding
coordinates. This graph shows clearly that there are three
clusters of variables: 1, 2, and 3; 4 and 5; and 6 and 7.
The graph makes it clear that variables 1, 2, and 3 consti
tute a separate cluster from those of other variables. That
is, variables 1, 2, and 3 are clustering on Factor 3, which
is distinct from the other two clusters, regardless of the
fact that the absolute loadings of variables 1, 2, and 3 are
heavier on Factor 2 than on Factor 3. Variables 4 and 5 are
closer to Factor 2 axis than all other variables. This in
dicates that variables 4 and 5 are more relatively loaded
and are clustered on Factor 2, and their association with
this factor is closer than with Factor 3, which is also
i.oi
. 9".
. 8
. 7
. 6
. 5
.4
. 3
. 2
. 1
67
Factor 3 x.
Factor 1
Factor 2
.3 .4 .5 .6 ->«r**"
.8 .91.0
Fig. 1.--Clusters of seven hypothetical variables on three factors extracted from the illustrative correlation matrix presented in Table 1.
obvious in Table 3 (their loadings on Factor 2 are 0.6 3 and
0.67 respectively, while the corresponding loadings are 0.02
and zero only on Factor 3). The clustering of variables 6
and 7, clearly seen in Table 3, is emphasized by the graph
and represents the third cluster of variables.
The above discussion show that examination of the
table together with the graph of rotated factor loadings can
be effectively used in determining the group of variables
clustered on each extracted factor. After the variables'
clusters are determined, TcUDle 3 may be reorganized to show
only the loadings of the variables that are clustered on the
-I Tl < :.9
-I \
J }
68
three factors, with the loadings arranged in a descending
order, as shown in Table 4 below. This latter table shows
the clusters with great clarity, which is a convenience to
the reader.
TABLE 4
HIGHEST LOADINGS OF SEVEN HYPOTHETICAL VARIABLES ON OBLIQUELY ROTATED THREE FACTORS EXTRACTED FROM THE ILLUSTRATIVE CORRELATION MATRIX PRE
SENTED IN TABLE 1
Variabl
6
7
5
4
3
2
1
es Fac
1
0.
0.
tor
85
85
Factor 2
0.67
0. 63
Factor 3
0.56
0. 54
0.51
Interpretation of the results obtained from factor
analysis requires that rotated factors be identified, ex
plained, and renamed in order to be used for further anal
ysis or for more understandable communication and generali
zation. Describing and renaming rotated factors should re
flect the nature of disclosed patterns of relationships, and
the substance of the variables involved in each pattern or
factor. Reflecting these patterns, represented by rotated
•'•Ibid., p. 475.
69
factors, depends upon the nature and characteristics of the
variables clustered on each factor. The nature of variables
6 and 7, in the above discussion for example, should help in
explaining and renaming Factor 1, variables 4 and 5 in ex
plaining Factor 2, and variables 1, 2, and 3 in explaining
Factor 3. In regard to the illustrative example discussed
in this chapter, rotated factors cannot be explained or re-
ncimed because of the hypothetical nature of the excimple and
the lack of adequate information necessary for this purpose.
IX. Summary
In siimmary, factor analysis is a mathematical tech
nique which possesses the power of reducing a large number
of variables to a more manageable number of factors that ac
count for the association among the variables. The few
underlying factors identified by the analysis may then be used
as points of emphasis in providing a solution to the problem
on hand. As applied to the materiality problem, factor anal
ysis is used to identify the factors underlying the income
statement accounts in the retail trade industry and account
ing for the intercorrelations among them. Each factor will
represent a group of income statement accounts. These fac
tors or groups of accounts resulting from factor analysis
are then used as a basis of devising more objective, than
presently existing, materiality criteria.
The assumptions made in this study comply with the
70
basic assumptions of factor analysis. These assumptions are
the existence of: linear relationships, a degree of corre
lation among the variables, and variability in the data.
The Thurstone model, which uses the centroid method
of factor extraction, and the principal component technique,
used in this study, are but two of a number of factor models
that may be used to analyze intercorrelations among variables
Extracted factors are then rotated orthogonally or obliquely
to enable the identification of variables' clusters on these
factors. The results of factor analysis, represented by
rotated factors, are then described and reneimed for under
standable communication and generalization.
The reader would remember, at this stage, that fac
tor analysis has served its purpose of determining variables'
clusters or underlying factors accounting for the intercor
relations among the variables in this study. Therefore,
Table 4 above presents the final results of factor analysis
that will be used as a basis of setting up criteria for
measuring materiality in accounting, as indicated earlier in
Chapter II. The following chapter will give the application
of factor analysis to the empirical data collected for the
purpose of this study, as determined in the first two chap
ters. It also applies the steps following factor results
for determining the criteria for materiality decisions.
CHAPTER IV
FACTOR ANALYSIS RESULTS AND MATERIALITY CRITERIA
I. Introduction
There are two major objectives to this study. The
first objective is to investigate the existing materiality
criteria the result of which is presented in Section I of
Chapter II. The second objective is to demonstrate the ap
plicability of factor analysis to solving the materiality
problem in accounting. As mentioned earlier, any industry
may have been used to illustrate the techniques suggested in
this study. The retail trade industry has arbitrarily been
selected to illustrate the application of factor analysis to
solving the materiality problem.
The Fairchild's Manual of Retail Stores has been
used to identify available population in the retail trade in
dustry to be analyzed. This manual has been used because it
was the only reference manual at Texas Tech Library that
contains, exclusively, information on a large number of re
tail firms. After excluding foreign companies and divisions
of the retail companies listed in the Fairchild's Manual,
the remaining number of companies representing the population
i
Fairchild's Financial Manual of Retail Stores
71
72
of this study is 600. This number includes 350 parent com
panies and 250 subsidiaries.
A questionnaire has been designed to collect infor
mation on selected twenty-five income statement accounts.
The purpose of the questionnaire is to obtain an estimate of
the selected twenty-five income statement accounts balances,
in weights form ranging from 0 to 10, for the latest com
pleted accounting year.
This chapter will present the results of mailing the
questionnaire designed for collecting the data needed for
this study and the results of factor analysis of the data re
ceived. It will also present the resulting materiality cri
teria based on factor analysis. The last part of this study.
Chapter V, then will present the sximmary, limitations, and
conclusions of the study.
II. Data Compilation
The questionnaire was mailed to each one of the 600
companies, on January 23, 1973, in the hope that at least 133
responses would be received to satisfy 0.95 confidence level 2
or 101 responses for 0.90 confidence level. By February 7,
the deadline for receiving responses, only seventy responses
were received. Therefore, a second request was mailed to 2 Discussion and computation of this sample size is
presented in Appendix III. The total number of responses received was eighty-
two, of which twelve were incomplete and hence excluded from this study.
73
these companies. To avoid double responses from the same
respondents, the second request included an additional sen
tence asking for responses from only those who had not ans
wered the first request. The number of responses received
from the second request, after the end of its deadline on
February 17, amounted to twenty-nine, of which five responses
were incomplete and thus, were excluded. In other words,
the total number of responses received from the two mailings
of the questionnaire was ninety-four (approximately 16 per
cent of the population). This relatively low response per
centage may be attributable to the detailed information re
quired by factor analysis and the existence of more than 41
per cent subsidiary companies in the population, some of
which are asked by their parent companies not to give any
unpublished financial information. Four respondents indi
cated that the required data were much detailed, and two
respondents said that their parent companies prevent them
from providing any informative financial data. The ninety-
four responses received satisfy a confidence level very
close to 0.90 (0.885).
As very few respondents (less than 14 per cent) as
signed weights to the last four accounts in the questionnaire
(extraordinary gains or losses, results of transactions with
affiliates, profit or loss on sale of fixed assets, and
profit or loss on sale of securities including treasury
stock), these accounts have been excluded from the analysis.
74
The interest and dividends earned account is also dropped
from the analysis because only 31 weights have been assigned
(less than 33 per cent of total responses).
III. Factor Analysis of the Data
The data on the remaining twenty income statement
accounts have been factor analyzed at the Computer Center at
Texas Tech University. The factor analysis programs utilized
are type PAl and PA2. The only difference between these two
programs is that the latter uses an iterative process to
estimate the communalities to be entered in the principal
diagonal before the factor extraction process starts. Pro
gram PAl, on the other hand, does not change the unity
entered in each cell of the diagonal of the correlation ma
trix. These two programs follow the general procedure of
the principal component method of factor extraction suggested 4
by Hotelling who developed this method in the 1930's.
Any factor analysis starts with a correlation matrix.
The correlation matrix computed from the received data to
gether with the arithmetic mean and standard deviation of
each variable are shown in Table 5. The procedure used in
computing the correlation coefficients is the product-moment
method of Pearson. In order for the study to account for the
^Harold Hotelling, "Analysis of a Complex of Statistical Variables into Principal Components," Journal of Educational Psychology, XXIV (1933), pp. 417-41 and 498-520. Harry H. Harman, Modern Factor Analysis, (Chicago: The University of Chicago Press, 1967), gives the details of this method in Chapter VIII.
75
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76
complete variance of all the data, unity has been entered
in the principal diagonal of the correlation matrix. As
mentioned earlier in Chapter III, the correlations above the
diagonal are identical with those below it.
The next step then is to extract the underlying fac
tors using the principal component method. Unrotated factor
loadings of the extracted seven factors are listed in Table 6
together with their corresponding eigenvalues and percentage
of variance accounted for by extracted factors. Eigenvalue-
one criterion has been used in extracting the factors to de
termine the number of factors to be extracted. Factor ex
traction will stop when the eigenvalue of the last factor
extracted falls below unity. Only factors with equal to or
greater than unity eigenvalues will appear in the unrotated
factor loadings table to be rotated in the succeeding step.
The number of factors that conforms with this eigenvalue-one
criterion (seven factors) and their factor loadings appear
in Table 6. This table shows that the seven extracted fac
tors accoxint for 100 per cent of the variation in all the
2
data. The communalities column named h gives the propor
tion of variation in each variable represented by the seven
extracted factors.
In order to identify the variables loaded on each
one of these seven factors, the varimax rotation has been
^Fruchter, Introduction to Factor Analysis, p. 99.
77
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78
used cind the rotated factor loadings are shown in Table 7.
The clusters of variables are clearly seen in this table
and are summarized, for convenience, in Table 8. Table 8
shows that some of these factors have only one variable in
volved (Factors 2 and 5), others have two variables (Factors
3 and 7). Since the seven-factor solution is not markedly
different from the five-factor solution, as shown later in
this section, and in order to keep the number of clusters at
a minimum, the solution of extracting five factors only has
been considered. The reason and methodology of reducing the
number of extracted factors from 7 to 5 are discussed later
in this Section. Unrotated factor loadings of the five-factor
solution are given in Table 9. It is noticed that the five-
factor loadings in Table 9 are different from the first five-
factor loadings of the seven-factor solution presented in
Table 6. The reason for this difference is that factor anal
ysis computer program PA2 was used in the seven-factor solu
tion while program PAl was used in the five-factor solution.
The reason for using different programs is to reduce the num
ber of clusters to a minimum. The only difference between
the two programs, as mentioned earlier, is that PA2 uses an
interative process to estimate the communalities to be
entered in the principal diagonal of the correlation matrix
before starting factor extraction. Program PAl, on the
other hand, does not change the unity entered in the prin
cipal diagonal. Table 9 shows that 72.7 per cent of the
r
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79
v o o v o m r - f N j o D i ^ v D v D c N i v D ' v r ^ o o r o m r H r ^ v x )
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80
TABLE 8
CLUSTERS OF SELECTED TWENTY INCOME STATEMENT ACCOUNTS ON SEVEN PRINCIPAL FACTORS
EXTRACTED FROM THE EMPIRICAL CORRELATION MATRIX PRE
SENTED IN TABLE 5
Factor 1
6
7
8
14
17
Factor 2
9
Factor 3
3
4
Factor 4
10
11
12
16
18
19
Factor 5
13
Factor 6
1
2
20
Factor 7
5
15
total variance in the data is represented by the five fac
tors. The analysis of the rotated factor loadings of the
five-factor solution, however, has special significance.
Table 10 of rotated factor loadings of the five factors shows
the following clusters appearing in Table 11. The clusters
of the oblique rotation in Table 10 are identical with the
clusters of the varimax rotation except that the sequence of
factors three and four is reversed in the varimax rotation.
It is obvious in Table 10 that all the variables are clearly
involved in specific factors except variable 1 (net sales)
which is approximately equally loaded on more than one factor
(Factors 1, 2 and 4). The graphical presentation of the
clusters given in Figures 2 through 4 shows that variable 1
is closer to the variables 9, 13, and 20, which are
81
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O O r H H O O O O O O O O O O O O O O O O I I I I I I I
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o o o o o o o o o o o o o o o o o o o o I I I I I I I I I I I I I I
v O r H ^ ' d ' i n r ^ r ^ c M O O v o v D O O r o o o c M c y ^ r - v o o r * > o o o o r H r H O i - H i n i n i n r H O o r ^ r o c o r ^ o
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83
TABLE 11
CLUSTERS OF SELECTED TWENTY INCOME STATEMENT ACCOUNTS ON FIVE PRINCIPAL FACTORS EXTRACTED
FROM THE EMPIRICAL CORRELATION MATRIX PRESENTED IN TABLE 5
Fact
1
10
11
12
16
18
19
or Fact
2
1
2
9
13
20
or Factor
3
3
4
Factor
4
6
7
8
14
17
Factor
5
5
15
exclusively clustered on Factor 2, than to any other cluster.
Therefore, variable 1 is considered to belong to Factor 2 I
cluster. Only three figures of factors' combinations have i»
been presented because they show the clusters more clearly j
than other possible combinations of the factors.
The significance of the five-factor solution becomes ^ I
obvious when Table 8 (ousters of seven factors) and Table 11 » 9
(clusters of five factors) are compared. It may be noted
that in the seven-factor solution. Factor 1 cluster is iden
tical with Factor 4 cluster in the five-factor solution (var
iables 6, 7, 8, 14, and 17). The clusters of Factors 3, 4,
and 7 of the former solution are also identical with the
clusters of Factors 3, 1, and 5 of the latter solution re
spectively. The only difference between the two solutions
is that three factors of the seven-factor solution (2, 5,
84
+ 2 1.0b.
.9-
.8.
. 7
.6-
I I C 9 J
I 1
1
Factor 2
Factor 1 Horizontal Factor 2 Vertical
Fig. 2.--Clusters of selected twenty income statement accounts on two of the five principal factors extracted from the empirical correlation matrix presented in Table 5.
85
+ 4
1.0
.9
.8
. 7
.6
. 5
.4K
.3 '
-1 Factor
1. 0. 9 £ .7 .5 .4 .3 .2 .1
Factor 2
Factor 1
1
Factor Vertical
Fig. 3.--Clusters of selected twenty income statement accounts on the five principal factors extracted from the empirical correlation matrix presented in Table 5.
86
- 2
1.0 9
Factor 2
16>
18
+ 4
1 . 0-
. 9 .
. 8-
. 7.
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Factor 2 Horizontal Factor 4 Vertical
Fig. 4.--Cluster of selected twenty income statement accounts on Factor 2 of the five principal factors extracted from the empirical correlation matrix presented in Table 5.
87
and 6) are consolidated in Factor 2 of the five-factor solu
tion. Combining the three factors of the former solution in
one factor of the latter solution makes the cluster more
meaningful. It involves the accounts: sales, purchases,
rent, advertising, and income tax which have an important
common characteristic related to the size aspect of the busi
ness activities. Therefore, it is believed that the five-
factor solution would be more desirable on the basis of
bringing these five variables into one cluster and thus mak
ing the cluster more meaningful by bringing out more clearly
this important characteristic. It would be desirable also
because it reduces the clusters from seven to five without
affecting the results markedly. And finally, the result of
this combination will be a smaller number of materiality
criteria which depends on the number of clusters. The re
sults of clustering the twenty variables on the five factors
are presented in Table 12 which shows only the loadings of
the variables that are clustered on the five factors, with
the loadings arranged in a descending order.
The step that follows the identification of the vari
ables' clusters is the description or interpretation of the
five identified factors. Interpretation of the factors de
pends upon the components of each factor and their common
characteristics. This interpretation or renaming process
is perhaps the most difficult aspect of factor analysis be
cause an extracted factor may include several variables of
88
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89
different characteristics, and thus will be very difficult
to explain by using one name or phrase. It involves the ex
ercise of subjective judgment in order to arrive at names de
scriptive of the variables clustered on each factor. It
would be helpful in describing the factors, however, to con
sider the highly loaded variables that are involved in the
factor and those variables that have zero or near-zero load
ings and are thus unrelated to the factor.
The variables that are highly loaded on Factor 1 are:
insurance expenses, supplies, professional services, trans
portation, interest expense, and bad debt expenses. The
variables that have near-zero loadings on this factor are:
purchases, inventories, payroll, maintenance, utilities, and
income taxes. Giving consideration to the characteristics
of both related and unrelated variables, this factor seems
to be related to the period variable expenses closely re
lated to credit sales.
Factor 2 involves high loadings from variables 1, 2,
9, 13, and 20 (sales, purchases, rent, advertising, and in
come taxes). Variables unrelated to this factor, on the other
hand, are inventories, insurance, supplies, general expenses,
and bad debts. Consideration of the unique characteristics
of both groups of variables reveals the important aspect of
this cluster which is related to the size quality of busi
ness activities.
Since Factor 3 includes only beginning and ending
90
inventories, it may be simply named "inventories." The char
acteristics of the variables highly loaded on Factor 4 (pen
sion expenses, depreciation, maintenance, utilities, and
property tax) and of those unrelated to this factor (inven
tories and rent expenses), on the other hand, seems to be
related to the fixed, uncontrollable service type expenses.
Finally, Factor 5 which includes payroll and general expenses
but is unrelated to inventories, pension expenses, transpor
tation, interest expenses, and income tax, seems to be re
lated to controllable-unallocable human and communication
service expenses.
The above analysis and interpretation indicates that
net income of the business may be determined or explained in
terms of the five determined or explained powers or factors.
These factors may be the important factors that influence or
determine net business income in the retail industry. It
should be admitted, however, that this interpretation is
highly tentative.
JV. Materiality Criteria Based on Factor Analysis Results
At this stage, factor analysis has served its pur
pose of providing the groups of accounts clustered on the
basis of their intercorrelations. Following the completion
of the factor analysis, the second part of the analysis be
gins. This part of the analysis consists of using the iden
tified groups of accounts as the basis of devising materiality
91
criteria. Establishing materiality criteria will be discus
sed in the following sections of this chapter according to
the following steps which have been discussed in detail in
Section III of Chapter II:
1. Determine the contribution of each one of the
five groups of accounts to business net income.
2. Compute the absolute sum of every one of the
five groups of accounts.
3. Equalize the effects of the five groups of ac
counts on net income.
4. Put the reciprocal of absolute contribution of
each group to net income (henceforth will be called the
multiple of the group) in a percentage form relative to the
total of the five multiples.
5. Determine the maximum allowable departure from
standard accounting practice, using the E/P ratio, for each
one of the five groups of accounts.
6. Convert maximum allowable departure of each
group into percentage materiality criteria.
A. Groups' Contributions to Net Income
The first step in establishing materiality criteria
is to measure the contribution of each group of accounts to
net income. This contribution is the measure of the nature
aspect of materiality of the particular group. This measure
is computed by adding the revenue or profit accounts of each
92
group on one side, then subtracting the expense or loss ac
counts of that group from revenue total. The revenue and
expense amounts used in computing the contribution of each
one of the five groups to net income are in weights terms
ranging from 0 to 10. The weights are those assigned by the
ninety-four chief accountants in the retail trade industry who
contributed to this study. The weights used in computing con
tributions to net income are the arithmetic means of each one
of the income statement accounts. The purchases weight
used in computing the contribution of Group 2 to net income,
for example, is the arithmetic mean of the 94 weights assigned
to purchases by the 94 respondents (6.59 weights).
The contribution of Group 1 to net income, for ex
ample, is the difference between the total of the revenue
accounts in Group 1, which is zero, and the total of the ex
pense accounts, which is 0.4532 (the total of the arithmetic
means of the accounts involved, 10, 11, 12, 16, 18, and 19,
which are: 0.0645 + 0.0795 + 0.0494 + 0.0985 + 0.1249 +
0.0364 = 0.4532). Since all of the accounts involved in
Group 1 are expenses, the total contribution of this group
to net income will be negative (-0.4532). The same procedure
is followed to determine the contribution of each of the
five groups of accounts and the results are shown in Table
13. The total contributions of all the groups are shown at
^A list of the twenty income statement accounts used in the analysis, their arithmetic means in weights terms, and their standard deviations are presented in Appendix II.
93
the bottom of the table. This total is the net income of
the business in the retail industry on the average in weights
terms.
TABLE 13
NET CONTRIBUTIONS OF THE FIVE GROUPS OF ACCOUNTS TO BUSINESS NET INCOME
Group Contribution
1 -0.4532
2 2.6875
3 0.1009
4 -0.4950
5 -1.5597
Total (Net Income) 0.2805
B. Groups' Absolute Sums
The second step in establishing materiality criteria
is to compute the absolute sum of the accounts involved in
each group to determine the size aspect of materiality of
each group. The absolute sum of the group is computed by
adding up the arithmetic means of all the accounts in the
group without consideration to the nature of the account
(expense or revenue). The absolute sum of the accounts in
Group 1, for example, is |0.4532| (the sum of the arithmetic
means of the accounts 10, 11, 12, 16, 18, and 19 that are in
volved in Group 1: 0.0645 + 0.0795 + 0.0494 + 0.0985 + 0.1249
+ 0.0364 = |0.4532|). By following the same procedure, the
absolute sumes of the five groups are shown in Table 14.
94
TABLE 14
ABSOLUTE SUM OF THE ARITHMETIC MEANS OF THE FIVE GROUPS OF ACCOUNTS
Group Absolute Sum
1 0.4532
2 17.3125
3 3.7781
4 0.4950
5 1.5597
Total 23.5985
The absolute sum of a group represents the size of the group
of accounts, in its unique mix, that has produced the cor
responding contribution to net income computed in the pre
ceding step. The absolute sum of Group 2 (17.3125), for
example, is the total amount of weights or dollars, in its
unique mix of accounts and proportions, that is necessary
to produce 2.6875 weights or dollars contribution to net
income.
C. Groups' Equalized Effects on Net Income
The purpose of the third step is to equalize the ef
fects of the individual groups on net income. In other words,
the purpose is to determine the absolute sum of each group
which is required to produce one dollar or weight of net in
come. As mentioned earlier in Chapter II, this equalization
process is accomplished by multiplying both the net contribu
tion (determined in step A above) and the absolute size of
95
each group (determined in step B above) by the reciprocal
of the contribution of the particular group to net income
(group multiple). In order to equalize the effect of Group
1, for example, with the effect of other groups, the net
contribution (-0.4532) and the absolute size of this group
(|0.4532|) are multiplied by the group multiple (1/0.4532)
disregarding its sign, and the result will be -1 weight or
dollar of net income (negative income means loss) produced
by a combination of accounts in Group 1 amounting to |1|
weight or dollar. Following the same procedure for the five
groups produces the following equalized effects shown in
Table 15. The equalized absolute sum of Group 2 (7.2227)
means that 7.222 7 weights or dollars mix in this group will
produce 1 weight or 1 dollar of net income. This equalized
absolute sum has significance equal to one weight or one
dollar of Group 1 (or Group 4 or Group 5) mix that produces
equal but negative amount of net income (one weight or dollar)
TABLE 15
EQUALIZED EFFECTS OF THE FIVE GROUPS ON NET INCOME
Equalized Unity Group Absolute Sum Contribution
1
2
3
4
5
1.0000
7. 2227
37.4440
1.0000
1.0000
-1
1
1
-1
-1
96
D. Groups' Multiples
The fourth step in establishing materiality criteria
is to put the multiples of the absolute sums and net contri
butions of the five groups (1/0.4532 for Group 1, 9/2.6875
for Group 2, . . .) in percentage form relative to their own
total. The purpose of this transformation is just to pro
vide greater convenience for later computations. This is
done by relating the multiple of each group to the total of
these multiples by adding the multiples of the five groups
(1/0.4532 + 1/2.6875 + 1/0.1009 + 1.0.0495 + 1/1.5597 =
2.2065 + 0.3721 + 9.9108 + 2.0202 + 0.6411 = 15.1507), divid
ing each multiple by this total, and multiplying each pro
duct by 100. Applying this procedure to the multiples of
the five groups provides the following percentages in Table
16. These percentage multiples mean that a percentage por
tion of a particular group (4.2314 per cent of the accounts
in Group 5) produces a contribution to net income equal to
that produced by the percentage portion of another group
(13.3341 per cent of the accounts in Group 4). The percent
age multiple of Group 1 (14.5631) means that 14.5631 per
cent of the accounts involved in Group 1 produces a contri
bution to net income equal to the contribution produced by
2.4 559 per cent of the accounts involved in Group 2, which
in turn equals the contribution produced by 6 5.4149 per cent
of the accounts in Group 3 (algebraic signs not considered).
97
TABLE 16
TRANSFORMING GROUPS' MULTIPLES TO PERCENTAGES OF THEIR TOTAL
Group
1
2
3
4
5
Multiple
2.2065
0. 3721
9.9108
2.0202
0.6411
Per Cent of
14.5631
2.4559
65.4149
13.3341
4.2314
Total
%
%
%
%
%
Total 15.1507 100.0000 %
E. Maximum Allowable Departure from Standard Practice
The portion of net income considered as the dividing
line between material and immaterial total dollar effect of
7
departure from standard accounting practice (5.92%) is com
puted from the average net income of the retail industry
(0.2805 weights or 2.805 per cent of net sales) by adding
the arithmetic means of revenues and subtracting total arith
metic means of expenses from total revenues as determined
by the questionnaire results. This net income (2.805 per
cent of sales) is very close to the average of net income
of a random sample of fifty companies drawn from the same p
industry (2.74 per cent of 1971 sales). The portion of net
^The reasons for using this ratio (E/P) and the computations involved are discussed in Chapter II.
^Fairchild's Financial Manual of Retail Stores.
98
income (5.92 per cent of 0.2805 or 0.016605) in terms of
weights represents the maximum allowable departure from
standard accounting practice in the books. If the total
dollar effect of known or discovered departure from stand
ard accounting practice in the books of the business equals
or exceeds 0.016605 weights, the departure should be con
sidered material and be corrected or disclosed. This maxi
mum allowable dollar effect of departure from standard prac
tice (0.016605) is then divided among the five groups ac
cording to their significance as determined by the percent
age multiples, computed in Section D above, in order to de
termine the amount of maximum allowable dollar effect of
departure from standard practice for each group. Table 17
shows the results of this allocation, as the maximum allow
able total dollar effect of departure from standard practice
for each one of the five groups of accounts. The maximum
allowable dollar effect departure for Group 1, for example,
is computed by multiplying maximum total dollar effect of
departure from standard accounting practice in the books
(0.016605) by the percentage multiple of Group 1 (14.5631%)
to produce 0.002418 as shown in Table 17. Total dollar ef
fect of departure from standard accounting practice in a
group should not equal or exceed the maximum given in Table
17. If the total dollar effect of departures in Group 1,
for example, equals or exceeds 0.002418 weight, it should be
corrected or disclosed.
99
TABLE 17
MAXIMUM ALLOWABLE TOTAL DEPARTURE FOR THE FIVE GROUPS OF ACCOUNTS
Maximum Allow-Group able Departure
1 0.002418
2 0.000407
3 0.010862
4 0.002214
5 0.000702
Total 0.016603
F. Percentage Materiality Criteria
The final step in establishing materiality criteria
is to put these maximum limits of dollar effect on departure
from standard accounting practice for each group in percent
age form relative to the absolute sum of each group computed
in Section B. The purpose of this step is to facilitate
using the criteria for individual accounts in each group.
This purpose is accomplished by dividing the maximum allow
able dollar effect of departure from standard accounting
practice of each group (computed in Section E) by the cor
responding absolute sum of the group (computed in Section B).
The percentage materiality criteria for Group 1 is computed
by dividing its maximum allowable dollar effect of departures
(0.002418) by its absolute sum (0.4532) to produce 0.533539%.
This means that 0.533539%, the percentage criteria of this
group, will apply to any account involved in Group 1. Any
100
dollar effect of departure from standard accounting practice
that equals or exceeds this percentage of the account, from
this group, should be considered material and thus should
be corrected or disclosed. Table 18 shows the percentage
materiality criteria for the five groups. Supplies expenses,
for example, is one of the accounts involved in Group 1. If
at any time the balance of this account is $10,000 and there
is a decision to be made at that time concerning whether an
amount spent on buying tools for $100 should be charged to
tools (an asset) or to supplies (an expense), the 0.533539
per cent criterion should be used. Since the tools cost is
1 per cent of supplies expenses balance and this is greater
than the 0.533539 per cent criterion, the amount will be
considered material and should be charged to the tools ac
count (an asset) rather than a supplies expense. Otherwise,
the entry will be erroneous and should be disclosed.
TABLE 18
PERCENTAGE MATERIALITY CRITERIA FOR THE FIVE GROUPS OF ACCOUNTS
Group Per Cent of Criteria
1 0.533539 %
2 0.002350 %
3 0.287499 %
4 0.447272 %
5 0.045008 %
101
G. Applicability of Materiality Criteria
Percentage materiality criteria for a group applies
to all the accounts involved in the group. Any dollar ef
fect of departure from standard accounting practice in net
sales, for example, that equals or exceeds 0.00235 per cent
of net sales (Group 2) will be material. This criterion
should also apply to the components of the account involved,
i.e., sales returns or sales discount will be subject to the
same criterion applicable to net sales. The criteria should
apply also to accounts not explicitly mentioned in this
study but which approximate the nature or properties of any
of the five groups, or to the accounts which constitute the
basis of computing the accounts analyzed in this study. Com
putation of depreciation expense, for example, is based on
the cost of the particular asset. Therefore, the criterion
that applies to depreciation expenses should apply to the
asset upon which depreciation is based. Consequently, any
dollar effect of departure from standard accounting practice
in the equipment account that equals or exceeds 0.447272
per cent (depreciation criterion of Group 4) should be con
sidered material.
In some cases, two materiality criteria may be simul
taneously applicable. In order to keep the total dollar ef
fect of departures from standard practice in the books with
in the maximum limit (5.92 per cent of net income), the cri
terion that produces the smaller dollar amount should be used.
102
If the materiality decision to be made concerns whether the
$100 purchased tools should be capitalized or expensed as
supplies, the tool asset criterion which is the same criter
ion of depreciation (0.447272 per cent of Group 4) will
apply, and the supplies criterion (0.533539 per cent of Group
1) will also apply. Therefore, if the tools balance is
$20,000, the maximum dollar effect of departures from stan
dard practice allowable in tools account will be $89.54
(0.447272 per cent of $20,000). If the supplies expenses
balance, on the other hand, is $10,000, the maximum allow
able dollar effect of departures in this account will be
$53.35 (0.533539 per cent of $10,000 supplies expenses).
Since the application of the supplies criterion provides a
lower limit to allowable dollar effect of departures from
standard practice, it should be used in this case. Conse
quently, the $100 tools should be capitalized because the
amount involved is greater than the $5 3.35 maximum allowable
dollar effect of departure from standard accounting practice.
H. Materiality Criteria in a Range Form
In order for the accountant to have some flexibility
in applying materiality criteria, as shown in Table 18, to
different circumstances, it may be desirable to have a range
of percentage materiality criteria rather than a single un-
flexible percentage. This range may be computed through
utilizing the standard deviations of the weights assigned to
103
the analyzed accounts as follows:
1. The arithmetic mean of standard deviations of
the accounts involved in each group is computed in order to
be used in establishing a probabilistic range of materiality
criteria. The average standard deviations for the five
groups appear in Table 19. These averages have been com
puted by dividing total standard deviations of accounts in
cluded in a group by the number of accounts involved, as
follows: accounts 1, 2, 9, 13, and 20 that are included in
Group 2 have 0.0000, 1.4756, 0.3531, 0.2381, and 0.2490 stan
dard deviations respectively. The total of these standard
deviations is 2.315 8 which produces an average standard de
viation of 0.46 3160 for Group 2 when divided by the number
of accounts involved (5).
TABLE 19
AVERAGE STANDARD DEVIATIONS OF THE FIVE GROUPS OF ACCOUNTS
Average Standard
Group Deviation
1 0.121850
2 0.463160
3 1.396650
4 0.112980
5 0.484000
104
2. For this standard deviation to be usable, it must
be converted into a percentage form relative to the absolute
sum of the arithmetic means of the same accounts involved in
the particular group, because the percentage criteria have
been computed in this form. Putting average standard devi
ations of the five groups in a percentage form relative to
the absolute sums of the arithmetic means of the same accounts
involved in each group is computed by dividing average stan
dard deviation of the group by the absolute sum of the arith
metic means of that group shown in Table 14. The relative
average standard deviation of Group 1, for example, is com
puted by dividing its average standard deviation (0.121850
from Table 19) by the absolute sum of its arithmetic means
(0.4532 from Table 14) which produces 26.8866 per cent. The
relative average standard deviations of the five groups are
shown in Table 20.
TABLE 2 0
RELATIVE AVERAGE STANDARD DEVIATIONS OF THE FIVE GROUPS OF ACCOUNTS
Standard Group Deviation
1 26.8866 %
2 2.6753 %
3 36.9670 %
4 22.8242 %
5 31,0316 %
105
3. Using a confidence level of 0.90, for example,
the confidence intervals of percentage criteria are computed
by adding and subtracting 1.645 standard deviations (in the
form determined above) from the percentage criteria of each
group. Applying this to the percentage criterion of Group 1,
the confidence interval for this group is computed as
follows:
Materiality Criterion of Group 1 ± 1.645
(Relative Average Standard Deviation) or
= 0.533539 ± 1.645 (0.268866)
= 0.533539 ± 0.442284
= 0.091255 and 0.975823.
This range means that the accoiintant can use a percentage
materiality criterion ranging from 0.091255 per cent to
0.975823 per cent in making his materiality decisions con
cerning any account involved in Group 1 according to dif
ferent existing circumstances. Within these two limits,
the accountant may use his judgment in making materiality
decisions.
The 0.9 0 confidence level used in establishing the
above range for Group 1 means that the accountant can be sure
90 times of 100 that the criterion based on the population
means of the accounts involved in the group will fall with
in the interval 0.091255%-0.975823%. Percentage materiality
criteria in a range form are shown in Table 21. It may be
noticed that the criteria intervals are wide. These wide
106
intervals are caused by the high dispersion in the weights
assigned to the twenty income statement accounts as re
flected by their large standard deviations shown in Appen
dix II.
TABLE 21
PERCENTAGE MATERIALITY CRITERIA IN A RANGE FORM
Group Range of Criterion
1 0 . 0 9 1 2 5 5 % t o 0 . 9 7 5 8 2 3 %
2 -0.041558 % to 0.046458 %
3 -0.320608 % to 0.895606 %
4 0.071814 % to 0.822730 %
5 -0.465461 % to 0.555477 %
The auditor, for example, may decide, according to
his judgment based on existing evidence, that estimated bad
debt expense (Group 1 account) should be $10,000. If he
finds that the actual book balance is only $9,950, he may
decide, under normal conditions, to use the average percent
age materiality criteria (0.533539 per cent which produces
a maximum limit of $53.35) and considers the $50 deficiency
as immaterial. But if he finds that the unemployment rate
in the country is increasing, the effect of which will in
crease the possibility of needing a higher bad debts ratio
than that of previous years, he may decide to use the lower
limit of the materiality criterion (0.091255%). According
to this decision the $50 deficiency in bad debts expense
107
will be considered material because it is greater than the
maximum limit $9.13 ($10,000 x 0.091255% = $9.13). However,
if the conditions are expected to be more favorable, the
auditor may decide to use the upper limit of the materiality
criterion of Group 1 and hence any deficiency less than $97.58
($10,000 X 0.975823% = $97.58) will be considered immaterial.
This criteria range of the five groups may be used
with high degree of flexibility according to the circumstances
under which the materiality decision will be made and ac
cording to the judgment of the accountant concerning exists
ing conditions. The ranges of the criteria that have a neg
ative lower limit may be attributable to the high degree of
variation in the weights assigned to the income statement
accounts. This issue may be solved in two ways:
(a) By using the lower of the single-point
criteria or the negative lower limit of the range as
the lower limit, or
(b) By using the single-point materiality
criteria as the lower limit instead of a negative
limit in such groups (2, 3, and 5).
The choice between these two suggested solutions
will also be left to the accountant's judgment according to
the then existing circumstances. It should be emphasized,
however, that the decision of choosing one solution or the
other should not affect the fact that total dollar effect of
departures from standard accounting practice in the books
108
should not exceed its maximum limit (5.92 per cent of net
income).
V. Summary
In summary, factor analysis of the empirical data
on twenty income statement accounts resulted in five groups
of accounts. The first group includes insurance, supplies,
professional services, transportation and freight, interest,
and bad debt expenses. This group has been explained as
being related to period variable expenses that are closely
related to credit sales. The second group includes sales,
purchases, rent, advertising, and income tax expenses. The
common characteristics of this group of accounts emphasizes
its close relationship with the size aspect of business
activities. The third group includes beginning and ending
inventories, hence named "inventories." The fourth group
consists of pension, depreciation, maintenance, utilities,
and property tax expenses. It has been suggested that this
group is related to the fixed controllable service type
expenses. And finally, group five, which includes payroll
and general expenses, has been explained as related to con
trollable-unallocable human and communication service ex
penses.
Based upon the results of factor analysis, the five
groups of accounts have been used to devise a more objective
materiality criteria than currently exist. Single-point
109
percentage criteria have been established and presented in
Table 18. For a more flexible criteria and to allow the use
of judgment in its application, ranges for materiality cri
teria have been established and shown in Table 21. The fol
lowing chapter will be the closing chapter of this study.
It will summarize the analysis, results, limitations, and
conclusions of the study.
CHAPTER V
SUMMARIES AND LIMITATIONS
I. Deficient Materiality Guidelines
Critical analysis of current literature on the con
cept of materiality indicates the existence of the concept
in accounting and auditing. It reveals, however, serious
difficulties in applying the concept to specific situations.
The review of the literature shows that several approaches
have been followed in an attempt to solve the application
problem of materiality. The Securities and Exchange Com
mission approach represents the rigid clear-cut prescription
of some guidelines for applying materiality to few situa
tions. The American Institute of Certified Public Account
ants approach, on the other hand, represents a neutral posi
tion. In general, it does not suggest any overall solution
to this problem and leaves it entirely to the judgment of
the accountant. Between these two extreme approaches lies
the accounting literature approaches of educators and prac
titioners. These latter approaches provide a wide range of
suggestions and proposals. Suggested guidelines vary sig
nificantly, however, among the various writers.
Accordingly, it is concluded that existing criteria
110
Ill
which guide the application of the concept of materiality
are deficient or are based on sheer judgment. The approach
of establishing materiality criteria suggested in this study
is based on statistically analyzing the association among
the accounts that determine net income. It takes into con
sideration both the size and the nature of the accounts in
determining their materiality.
II. Application of Factor Analysis
The utilization of the power of factor analysis of
clustering any large number of associated variables into a
few underlying factors has been suggested in this study to
solve the materiality problem. The procedure of devising
materiality criteria based on the ousters of income state
ment accounts was described in Chapter II. It is a two-phase
procedure. Phase one is concerned with clustering the twenty-
income- statement accounts into a smaller number of groups
based on their intercorrelations by utilizing factor anal
ysis. Phase two follows the results of factor analysis
(clusters of accounts) and incorporates the size and the na
ture of the accounts involved in the clusters in the pro
cess of devising the materiality criteria along the lines
discussed in Section III of Chapter II.
The retail trade industry has been used to demon
strate the application of factor analysis to solving the ac
counting problem of materiality. The weights assigned to
112
twenty-income-statement accounts by the chief accountants of
ninety-four retail firms have been used to correlate the
accounts to each other. The correlation matrix has then
been factor analyzed using the principal component method
of factor extraction. The five extracted principal factors
have been rotated orthogonally (varimax) and obliquely using
the algebraic solution to obtain the simple structure and to
facilitate the clustering of the accounts into five groups.
According to the loadings of the variables on the
five extracted factors, five groups of accounts were iden
tified. The first group of accounts, which is related to
period variable expenses that are closely related to credit
sales, includes the variables 10, 11, 12, 16, 18, and 19.
These variables represent the following expense accounts:
insurance, supplies, professional services, transportation
and freight-out, interest, and bad debts. The second group
of accounts is closely related to the size aspect of busi
ness operations. It includes the variables 1, 2, 9, 13, and
20 (sales, purchases, rent, advertising, and income tax ex
penses). Group three consists of the beginning and ending
inventories (variables 3 and 4). It has been named "in
ventories." The fourth group which seems to be related to
fixed, uncontrollable service-type expenses involves the
variables 6, 7, 8, 14, and 17 (pension, depreciation, main
tenance, utilities, and property tax expenses). The fifth
and final group consists of payroll and general expenses
113
(variables 5 and 15). Its peculiar characteristics seem to
represent controllable-unallocable human and communication
service expenses. It has been emphasized that the interpre
tation and renaming of the five groups should be considered
highly tentative, and further experiments will be needed to
support it.
III. Criteria Based on Factor Analysis
Definitions of materiality refer to facts that make
a difference in the judgment of a prudent investor in making
his investment decisions. Since investors use a number of
financial analysis ratios to base their decisions upon, the
E/P earnings rate ratio has been used in this study to deter
mine the dividing line between material and immaterial total
dollar effect of departure from standard accounting practice.
This ratio is significant to any financial analyst because
it is a major factor that motivates the investor to choose
among investment alternatives. It is very close to the ef
fective rate of return on investment because both the earn
ings per share and the share price are in terms of current
dollar value. The E/P ratio in the retail trade industry is
estimated at 5.92 per cent. As used in this study, it means
that 5.92 per cent of business net income is the maximum
allowable total dollar effect of departure from standard ac
counting practice in the books of the business. Departures
with a total dollar effect equal to or greater than 5.92
114
per cent of business net income should be considered mater
ial and be corrected or disclosed in notes to financial
statements or in the auditor's report.
Applying the estimated E/P ratio (5.92%) to esti
mated net income of the retail trade industry (0.2805 weights
or 2.805 per cent of net sales) produces 0.016605 weight.
This last amount (0.016605 weight) represents the maximxim
allowable departure from standard accounting practice in all
accounts of the business. This amount has been divided
among the five groups of accounts, according to their ma
teriality, in order to determine the maximum allowable de
parture in each group as explained in Chapter IV.
A. Single-Point Materiality Criteria
To enable the use of the criteria any time during
the accounting period without waiting until net income for
that period is determined, the criteria, based on last
period data, is put in a percentage form relative to the
absolute total of the group or cluster determined by fac
tor analysis and discussed in Chapter IV. The materiality
of any departure from standard accounting practice in any
account will be measured by multiplying the percentage cri
teria for the group that involves the particular account by
the account balance, at the materiality decision date, and
comparing the product (which represents the dividing line
between material and immaterial departure) with the dollar
115
effect of the departure under consideration. If the dollar
effect of the departure under consideration is less than the
criteria product, the departure is considered immaterial.
But if the dollar effect is equal to or greater than the
criteria product, the departure should be considered mater
ial and be corrected or disclosed. Percentage materiality
criteria for the five groups of accounts are shown in Table
18 in Chapter IV. This criteria is in a single-point form.
B. Range Form Materiality Criteria
Many accountants, however, believe that judgment is
vital and indispensable in making materiality decisions.
In order to recognize the importance of the accountant's
judgment and to allow for the exercise of professional judg
ment in making materiality decisions, the standard devia
tions of the twenty-income-statement accounts analyzed in
Chapter IV have been used to establish a range form of ma
teriality criteria. The confidence level desired for es
tablishing the confidence interval for materiality criteria
will be subject to the judgment of the accountant. Using
0.90 confidence level, for example, and the single-point
materiality criteria shown in Table 18 produces the confi
dence interval form of materiality criteria shown in Table
21. The range form materiality criteria allows for more
flexible use of the criteria and the exercise of judgment
in the light of the then existing circumstances. The single-
116
point criteria, for instance, may be used under normal cir
cumstances. But if the confidence in the accounting system
and controls is higher or lower, in the accountant's judg
ment, than it is in normal conditions, the accountant may
decide to use the upper or lower limit of the confidence
interval of materiality criteria respectively.
IV. Limitations of the Study
This study is concerned with demonstrating the ap
plicability of factor analysis to solving the materiality
problem in accounting. It has been limited to accounting
and auditing decisions concerning recording, classification,
and disclosure of financial facts in the retail trade indus
try. The results obtained from the analysis in the form of
materiality criteria may be used in the retail trade in
dustry with some caution and after giving careful consider
ation to its limitations.
The results of the study could have been more valid
and reliable if the number of responses received from the
accountants in the retail industry was larger than 94 (133
responses were required to satisfy a 0.95 confidence level
for inferences to be made based on this study). Improvement
of the results could have been attained also by utilizing
actual figures, rather than weights, and by using a larger
number of income-statement accounts (twenty accounts were
used in this study). Using more than one year data (five-
117
year average of the actual figures of income statement ac
counts) would provide even more reliable results. The limi
tations to achieving a higher degree of validity and reli
ability as related to the above mentioned points are the
lack of published detailed financial information, the con
fidentiality of detailed financial data, and the time and
cost factors.
The E/P ratio, used as the portion of net income that
divides between material and immaterial effect of departures
from standard accounting practice, is based on one-year data.
This ratio would be more valid and stable if it were based
on a longer period of time (five or more years). It was
extremely difficult to find five-year statistics on earnings
per share and market share price for an adequate number of
retail stores (133 stores to satisfy a 0.95 confidence level),
Consequently, the E/P ratio used in this study was based on
1972 statistics only.
Keeping these limitations in mind, the procedure
used in devising materiality criteria may be used in further
similar studies to provide support for the results of this
study. It may also be used to devise materiality criteria
for other industries that will facilitate the accountant's
decision-making process concerning materiality which is in
volved in almost all accounting decisions.
118
V. Recommendations
The resulting criteria based on the suggested ap
proach of solving the materiality problem is more objective
than the existing judgment-based criteria suggested by dif
ferent parties. This validity stems from the basis of es
tablishing the criteria by depending upon the association
among the accounts in grouping them, determining their sig
nificance, and finally establishing their materiality cri
teria. The criteria thus determined may be more valid and
stable, however, if the following steps are followed in fu
ture studies:
1. The nximber of accounts used in the analysis
should be as large and conclusive as possible; that is, more
detailed division of income statement accounts should be
used in the analysis. This condition is required by factor
analysis in order to provide better clusters of accounts and
for stronger generalizations based on the resulting clusters.
2. The data on the income statement accounts should
be more than one year in order to provide a more stable meas
ure of the accounts and the resulting criteria. A five-year
period would probably be adequate to reflect average general
business activities and normal earnings.
3. The dividing line between material and immateri
al total dollar effect of departures from standard account
ing practice should be based on a more than one year data
119
just as is recommended for the income statement accounts
mentioned in paragraph 2 above.
4. The materiality criteria based on relatively
long term statistics (five years of example) should be used
for future materiality decisions as long as the proportions
between each income statement account and net business in
come of the current year is not significantly different from
those of the five-year averages. When the difference be
tween the current year proportions and those of the five-
year averages is significant (as determined by statistical
tests), the criteria should be changed by using a moving
five-year average. The new criteria will be based on new
five-year averages for the latest five years. Materiality
criteria will need to be changed also whenever the current
E/P ratio is significantly different from the five-year
average. This recommendation should also apply to the cri
teria provided by this study. Whenever the difference be
tween the proportions of accounts to net income in this study
and those of any succeeding year is significant, a new cri
teria should be used based on the more current data.
5. Several experiments, similar to this study, will
be needed in order to support the clustering results of this
study and to establish the new names of the groups or clusters
of accounts. Renaming the clusters will be important to de
termine whether an account, not included in the analysis,
should belong to one cluster rather than the other, and
120
consequently what materiality criterion should be used for
such an account.
BIBLIOGRAPHY
Books
Adcock, C. J. Factorial Analysis for Nonmathematicians. Milborne: Milborne University Press, 1954.
Balsley, Howard L. Quantitative Research Methods for Business and Economics. New York: Random House, 1970.
Fairchild's Financial Manual of Retail Stores. New York: Book Division Fairchild Publications, Inc., 1972.
Fruchter, B. Introduction to Factor Analysis. Princeton, New Jersey: D. Van Nostrand Company, Inc., 1954.
Grady, Paul. Inventory of Generally Accepted Accounting Principles for Business Enterprises. Accounting Research Study No. 7. New York: American Institute of Certified Public Accountants, 1965.
Harman, Harry H. Modern Factor Analysis. Chicago: The University of Chicago Press, 1967.
Rummel, R. J. Applied Factor Analysis. Evanston: Northwestern University Press, 1970.
Schlaifer, Robert. Introduction to Statistics for Business Decisions. New York: McGraw-Hill Book Company, 1961.
Thurstone, L. L. Multiple-Factor Analysis. Chicago: University of Chicago Press, 1947.
. The Vectors of Mind. Chicago: The University of Chicago Press, 1940.
Webster's Third New International Dictionary. Springfield, Massachusetts: G. and C. Merriam Company, Publishers, 1967.
121
122
Government Publications
U.S. Securities and Exchange Commission. Regulation S-X, Form and Content of Financial Statements. Washing-ton, D. C : Government Printing Office, 1972.
Official Statements of Professional Accounting Groups
Accounting Principles Board. Earnings Per Share. Accounting Principles Board Opinion No. 15. New York: American Institute of Certified Public Accountants, 1969.
Accounting Principles Board. Reporting the Results of Operations. Accounting Principles Board Opinion No. 9. New York: American Institute of Certified Public Accountants, 1966.
Committee on Accounting Procedure. Restatement and Revision of Accounting Research Bulletins. Accounting Research Bulletin No. 43. New York: American Institute of Certified Public Accountants, 1953.
Executive Committee. Accounting and Reporting Standards for Corporate Financial Statements. Iowa City, Iowa: American Accounting Association, 1957.
Study Group on Audit Techniques. Materiality in Auditing. Toronto: The Canadian Institute of Chartered Accountan ts, 1965.
Periodicals
Bernstein, Leopold A. "The Concept of Materiality," The Accounting Review, XLII (January, 1967), 81-92.
Blough, Carman G. "Some Suggested Criteria for Determining Materiality," The Journal of Accountancy (April, 1950) , 353-54.
Chan, Stephen. "Materiality." The New York Certified Public Accountant, XXXI (June, 1961), 402.
Chetkovich, Michael N. "Standards of Disclosure." The Journal of Accountancy (December, 1955), 48.
123
Frishkoff, Paul. "An Empirical Investigation of the Concept of Materiality in Accounting." Empirical Research in Accounting: Selected Studies (1970), 117-25.
Gordon, Spencer. "Accountants and the Securities Act." The Journal of Accountancy (November, 1933), 438.
Griffin, Charles H. "Pedagogical Implications of the Materiality Concept." The Accounting Review, XXXIV (April, 1959), 299.
Hicks, Ernest L. "Some Comments on Materiality." The Arthur Young Journal (April, 1958), 11-16.
Hotelling, Harold. "Analysis of a Complex of Statistical Variables into Principal Components." Journal of Educational Psychology, XXIV (1933), 417-41 and 498-520.
Hylton, Delmer P. "Some Comments on Materiality." The Journal of Accountancy (September, 1961), 62-63.
Rappaport, Donald. "Materiality." The Journal of Accountancy (April, 1964), 43.
Reininga, Warren. "The Unknown Materiality Concept." The Journal of Accountancy (February, 1968), 31.
Sheth, Jagdish N. "Using Factor Analysis to Estimate Parameters." American Statistical Association Journal, LXIV (September, 1969), 808.
Woolsey, Sam M. "Judging Materiality in Determining Requirements for Full Disclosure." The Journal of Accountancy (December, 1954), 745-50.
APPENDIX
124
125
SIGNIFICANCE OF SAMPLE r
In order to test for the significance of a sample
coefficient of correlation, the null hypothesis is often
stated in the following form: the coefficient of correla
tion in the universe is zero, then effort is made to dis
prove it by showing that the coefficient of correlation in
the universe is significantly different from zero.
The T test may be used here because the distribution
of the coefficient of correlation r in the universe around
zero mean would be normal, and the sample size is relatively
large (greater than 30).
The T test formula is:
T = — - — = ry n - 1 ar
where
r = the sample coefficient of correlation
ar = the standard deviation of r
n = sample size
Computed value of T, in terms of standard normal
deviates, is then compared with the number of normal devia
tions corresponding to .95 confidence level (1.96). If com
puted T for any coefficient of correlation of a particular
Balsley, Quantitative Research Methods for Business and Economics, p. 25 8
126
account is greater than 1.96, the null hypothesis will be
rejected and the r under consideration proves to be signifi
cant, and thus qualifies the respective account to be in
cluded in the analysis.
As applied to this study, any coefficient of cor
relation greater than 0.203 will be significant as shown
below:
T = r J'n - 1 > 1.96
r7^94 - 1 > 1.96
0.65r > 1.96
r > 0.203
The sample size used in the above question is the
number of responses received and used in the analysis in
this study.
127
II
THE QUESTIONNAIRE AND RESULTS SUMMARY
January 23, 19 73
Dear Sir:
There are several accounting concepts that need to be clari-field to enable the accountant to apply them to practical situations. Research is needed in order to clarify such concepts. I am conducting research in accounting for my dissertation which I hope will be helpful to the accounting profession in the application of generally accepted accounting principles.
Would you please assign weights (ranging from 0 to 10) to each of the following accounts according to their dollar volume for the latest completed year in your company. The largest account should be assigned the weight (10). If net sales, for example, has the largest amount, it will be assigned weight (10) , and if depreciation is about one-half of net sales, it will be assigned weight (5), and if payroll expenses is approximately one-third of net sales, it will be assigned a weight of (3.33).
If any of the last four accounts is a loss, please add a negative sign to the left of the assigned weight.
The information you furnish will be considered confidential, and there is no need to type your address on the enclosed stamped return envelope.
Hoping to receive your completed questionnaire as soon as possible, or at least by February 7, your cooperation is highly appreciated.
Very truly yours,
Hamed M. Hadidi Texas Tech University
128
INCOME STATEMENT ACCOUNTS AND RESULTS' SUMMARY
Account Title Code Mean Standard Deviate
Net sales (gross less returns and allowances or discounts)
Net purchases Inventories on hand (beginning
of the year) Inventories on hand (end of
the year Payroll expenses (including salaries,
wages, commissions, and taxes) Pension and compensation plans
expenses Depreciation and amortization
expenses Maintenance and repair expenses
(for all purposes) Rent and lease expenses Insurance expenses (for all
purposes) Supplies expenses (all purposes) Professional services expenses
(legal, auditing, consulting. . .) Advertising and promotion expenses Utilities expenses (power, light,
and water) General expenses (telephone,
postage, miscellaneous) Transportation and freight-out
expenses (including travel) Property taxes and licenses Interest and other financing
expenses Uncollectible accounts expenses
(bad debts) Income tax expenses (federal
and other) Interest and dividends earned Extraordinary gains or losses Results of transactions with
affiliates Profit or loss on sale of fixed
assets Profit or loss on sale of secur
ities including treasury stock
1 2
3
4
5
6
7
8 9
10 11
12 13
14
15
16 17
18
19
20 21 22
23
24
25
10.00 6. 59
1.84
1.94
1.48
0.06
0.16
0. 09 0.32
0. 06 0. 08
0.05 0.18
0. 10
0.08
0.00 1.48
1. 35
1.45
0.88
0.08
0.17
0.14 0. 35
0. 06 0. 07
0.13 0. 24
0. 09
0. 08
0. 10 0. 09
0.12
0.04
0. 22
0. 0.
0.
0.
0. No answer No answer
18 08
18
,11
, 25
No answer
No answer
No answer
129
III
SAMPLE SIZE IN THE STUDY
The population used for this study consists of the
retail stores listed in Fairchild's Financial Manual of
Retail Stores (1972), after excluding Canadian companies,
foreign subsidiaries, and companies' divisions. The number
of this population is 600 companies, of which 350 are parent
companies aid 250 are subsidiaries. The questionnaire de
signed for collecting the data required for this study has
been mailed to each one of the 600 companies. Therefore,
this study is a census of the defined population. In order
for the results of the analysis, based on the data received,
to be reliable for inference purposes, there must be a min
imum number of returns from the mailed questionnaire to be
used in the analysis. This minimum depends upon the purpose
of mailing the questionnaire and the confidence level de
sired.
The purpose of mailing the questionnaire is to ob
tain estimates of the average value of each income state
ment account used in the analysis. The value of each ac
count, as required by the questionnaire, ranges from zero
to ten with an overall arithmetic mean of five.
Because of the absence of any information on the
distribution of income statement accounts and of expected
-^Fairchild's Financial Manual of Retail Stores.
130
large number of responses to be received and used (sample
size of more than thirty) the distribution of the accounts
may be assumed to be normal with no material loss of accu-2
racy. The standard deviation of a normally distributed
variable may be approximated by taking one-sixth of the
range of the values it might take." Therefore, the standard
deviation of this xiniverse may be approximated to be 1.6667
( ^ ^ ^ ^ ) ^ 6 ^ •
Computation of the minimum number of responses re
quired (sample size) requires a specific confidence level
such as 0.90, 0.95, or 0.99. A confidence level of 0.95
means that one can be sure 95 times out of a hundred that
the arithmetic mean obtained from received responses (sample
mean) will fall within the interval /ti 1.96ap, where>tis
the population mean and ap is estimated standard deviation
of the universe.
The minimiom number of responses (sample size) for
estimating the mean values of the variables in this study
is determined by the following formula:
2 Robert Schlaifer, Introduction to Statistics for
Business Decisions (New Yorkl McGraw-Hill Book Company, 1961), p. 309.
3 Balsley, Quantitative Research Methods for Business and Economics, p. 44.
4 Ibid., p. 99, adjusted for application to a finite
population by multiplying the infinite population formula zs 2 N
N = ^ by the correcting factor 1 - JTS—. P
131
N = i s AE.2 _ 1
zs' N
where
Ng = size of the sample
AE = estimated allowable error, or the amount the
sample mean is permitted to deviate from the
population mean
z = critical probability in terms of standard
normal deviates (1.96 for 0.05, 2.576 for
0.01, 1.645 for 0.10)
s = estimated standard deviation of the xiniverse
N = size of the universe P
The allowable error is estimated to be 5 per cent of
the population mean (5). This means that the study is con
cerned with a sample size that permits detecting up to 5
per cent deviations from the population mean (AE = 0.05 x 5 =
0.25).
With a 0.95 confidence level, the minimum number
of responses required is:
,, _ 1 s " 0.25 ,2 1
1.96 X 1.6667' 600
1
0.005856 -t- ^ 600
0.007523
= 132.9 or 133
132
If the confidence level is reduced to 0.90, the
sample size is:
N s . 0.25 .2 ^ 1 1.645 X 1.6667 ^°°
1
0.008314 + •"• 600
0.009981
= 100.2 or 101