Statistics, not Sadistics!

A Practical Guide to Statistics

for Non-Statisticians

By

James Riley Estep, Jr., Ph.D.

Professor of Christian Education

Lincoln Christian Seminary (Lincoln, Illinois)

Visiting Professor of Statistics

Southern Baptist Theological Seminary (Louisville, Kentucky)

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Table of Contents

2013 Edition

Section 1: Foundational Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Section 2: Overview of the Statistical Landscape . . . . . . . . . . . . . . . . . . . . . . 6

Section 3: Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Section 4: Inferential Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Section 5: Correlation Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Section 6: What to Look Out For . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

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Section 1

Foundational Concepts

Where do the numbers come from?

Education is at least in part based on theories derived from the findings of the

social sciences, e.g. learning, developmental, or administrative theories. Social science

research takes two different forms: Qualitative and Quantitative.1 Qualitative research

generates data in the form of words, e.g. interview transcripts, written descriptions of

observations, or historical documents; and is hence does not rely on statistical analysis.

Quantitative research generates numerical data, e.g. satisfaction rated on a scale of 1-5,

rankings, scores on standardized tests, or preparation times. The analysis of the

numerical data generated form quantitative research methods is called statistics.

Statistics is not just math. It is a specialized form of math. It is mathematics

applied to social science research, i.e. quantitative research. Statistics are also used in

the field of assessment, which is becoming increasingly important to educational

institutions and student standardized testing. This guide to statistics is not intended to

be an introduction or survey of quantitative research, nor is it intended to replace an

introduction to statistics textbook. Rather, this paper makes several assumptions:

You are in or have had a statistics class (such as the one may be in right

now).

You have access to a basic textbook on statistics that contains more in

depth material, especially the formulas. This paper will not show the

formulas since (a) most of you will use a computer and hence not even see

the formula, and (b) some of the formulas has very complex in detail, but

show nothing about their use in research.

You will do most of your statistical computations on a computer, using

Excel, SSPS

You make use of user-friendly websites like www.surveymonkey.com,

www.questionpro.com or the “dissertation helps” on

1 A third form of social science research may be considered the “mixed-method,” but this form

is in fact the intentional combination of qualitative and quantitative, and not really a new form

of research. However, mixed method is becoming the preferred form of social science research.

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www.leadership.sbts.edu; and so you don’t need to generate the numbers

yourself.

You will probably employ a statistician to do most of your “number

crunching” for a thesis or dissertation.

In any of these cases, you will still need to comprehend statistics, so as to design

the appropriate research and request the appropriate computations. In short, you have to

be smart enough to ask the statistician for the right stat! This paper is a crash course in

statistics for non-statisticians. It focuses more on understanding statistics than actually

doing the math.

Population, Sample, Soup and Statistics

“How was the soup?” Technically, you cannot tell the waitress how

the soup was, since you did not actually consume all the soup in the

pot (or at least I hope not). Rather, you base your response on the

bowl that was drawn from pot, only a sample of the soup that your

waitress provided. The population is the pot, and the sample is what

you draw from the pot. Sample size is important, so you need to stir the pot and use a

ladle to gather a suitable sample from which to draw your conclusion, since using just a

small spoon may not give you an accurate taste of the whole pot. Also, stirring the pot

before pulling out the sample is important, so as to guarantee that the appropriate

mixture of all the soup’s ingredients is represented. This is all part of the research

design.

All research design starts with a question, such as “What does the soup taste

like?” It is an unknown. We design research to gather data about the soup so as to

answer the question. It is concerned with the procedures that involve gathering

accurate data from a population being studied. The numbers used in statistics are

generated by doing quantitative research on a population or sample. Hence, the more

precisely a population is described and the more accurately a sample is pulled from the

population, the more accurate the numbers will be describing the population/sample.

For example:

QUESTION: How many hours does the average SBTS student study for

an exam in Greek 1 class?

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Figure 1.1

Since a researcher may not be able to

contact every student in Greek 1 (population),

he/she decides to randomly select a representative

group of Greek 1 students (sample) which is a

more manageable project. The survey is then used

on the sample to generate numerical data for

statistical analysis. A sample/population

calculator is available on www.leadership.sbts.edu

on “dissertation helps” and the “Articles and Resources” page. This resource will help

you avoid making a basic mistake in research design, and flaw the data upon which the

statistics are calculated. The findings of the survey are then reported based on

statistical analysis.

A Tale of Three “Datas”

Where do the numbers come from? Obviously quantitative research methods, as

described above. These numbers represent the reality being studied. But, not all

numbers are alike. It is critical to keep in mind the three kinds of data as they relate to the

three kinds of data: Categorical, Ordinal, Interval (also known as ratio).

Categorical/Nominal: Data separated into mutually exclusive categories; A scale

that “measures” in terms of names or designations of discrete units or categories.

o For example: age groups, gender, academic major

o Enables statistician to determine the mode, the percentage values, or a chi-

squared

SURVEY generating

numerical responses

Report

Findings

Statistical

Analysis

POPULATION

All students at

SBTS in Greek 1

SAMPLE

20 students

pulled from

population

???? DATA

Spoiler Alert:

If the entire population can be

reached, then one need only use

“descriptive statistics”.

However, if a sample is used,

inferential and/or correlative

statistics must be used, which

are far more complicated.

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Ordinal: Logically ordered categorical data; a scale that “measures” in terms of such

values as “more” or “less,” “larger” or “smaller,” but without specifying the size of the

interviews

o For example, a Likert scale surveys with Strongly disagree; Disagree;

Neutral; Agree; Strongly agree.

o Enables statisticians to determine the median, percentile rank, and rank

correlation.

Interval/Ratio: The distinctions between interval and ratio data are subtle, but

fortunately, this distinction is often not important. Certain statistical methods, i.e.

geometric mean and a coefficient of variation can only be applied to ratio data.

o Interval: A scale that measures in terms of equal intervals or degrees of

difference, but whose zero-point, or point of beginning, is arbitrarily established

(not absolute).

For example: Intelligence Quotient (IQ), since there is not real zero.

Enables statisticians to determine the mean, standard deviation, and

product movement correlation; also allows for most inferential statistical

analyses

o Ratio: A scale that measure in terms of equal intervals and an absolute zero-point

of origin.

E.g., birth weight in kilograms or a measurement of distance or height

Enables one also to determine the geometric mean and the percentage

variation; allows one to conduct virtually any inferential statistical

analysis.

These three kinds of data require different statistical treatment, e.g. certain

formulas only work with ordinal data rather than categorical. Mismatch the data with

the statistical formula . . . its like asking how many sides a circle has. The type of data

can also influence how data is presented and what kind of chart one uses to report

findings.

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Section 2

Overview of the Statistical Landscape

Not all Statistics are Alike!

Anyone who has traveled across country can readily tell

the difference between the United State’s southwest vs. the

Midwest vs. the deep South vs. New England. While certain

similarities exist in all three regions, distinctive geographic and

geological features mark the regions rather distinctively. The

American landscape is in fact s mosaic, a set of landscapes, each

with its own features, ecologies, and resources.

Statistics is a plural term. The statistical landscape consists of three distinctive

regions: Descriptive, Inferential, and Correlation. Table 2.1 provides a ready reference

to the basic idea of each of these three statistics (Sections 3-5 will address each in detail).

Statistics Type of Question: What is

X ?

Type of Question: What

are the odds of X

happening?

Type of Question: Are and

How Related are X and Y?

Statistics: Descriptive Statistics: Inferential Statistics: Correlation

Metaphor: Snapshot Metaphor: Gambling Metaphor: Thermometer

Formulas/Tests: Mean, Median, Mode, Range,

Quartile, Whisker-Box Plot, Z-

score, and Standard Deviation

Formulas/Tests: Hypothesis testing, p-value,

Z-test, t-Test, Chi-squared,

ANOVA (1-way and 2-way)

Formulas/Tests: Pearson r, Coefficient of

Determination, Scattergram;

Spearman rho, Kendall’s tau

Applications: “I want to

know what my congregation’s

membership is like?,” e.g. age,

height, weight, gender mix,

ethnicity, income levels, years

attending this congregation.

Applications: “Given the

average age of a congregation

member, what are the odds of

finding a 72 year old?” OR

“How sure am I that the

opinion of a sample of my

congregation about the new

program represents the whole

congregations?”

Applications: “Is there a

significant correlation

between the education level of

my congregation members

and their participation in

Sunday school?”

Table 2.1

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Descriptive Statistics

Descriptive statistics . . . describe. It is the most basic form of

statistical analysis of a body of numbers. “How many people

attend your church?” How do you respond? Do you read off

all the Sunday morning attendances for the previous year?

Probably not. Rather, summarize all those attendances into a

single number, the average attendance (statistically called the mean). “How did you do

in seminary?” You don’t recount your academic transcript; you probably give your

g.p.a. (grade point average) as a means of summarizing your academic performance

into a single, concise number. We use descriptive statistic most frequently and often do

not even realize it. Descriptive statistics are like a snapshot. “Tell me what you see?”

Descriptive statistics are used to summarize, analyze and share any set of numbers.

However, like a good photograph, you must be able to get everyone in the shot, or the

picture is incomplete. Descriptive statistics are useful only when the entire population

can be reached. While they are the basis of all the other forms of statistics, when you

only have a sample, descriptive statistics are not enough to reach a firm conclusion.

Descriptive statistics cannot answer all the questions or serve all our statistical needs,

and hence two other forms of statistics exist.

Inferential Statistics

What are the odds? Many of us have felt the frustration

of playing the board game Risk® and having a territory

defended by one single army that consistently rolls a 6 every

time against your superior forces. “What are the odds?”

“That’s not right!” “You’re cheating!” and the battle ensues. Inferential statistics are

typically used in regard to the probability of a response occurring. More specifically, if

a sample is pulled from a population, how certain can the researcher be that the

numbers gained from the sample accurately reflect the population being studied; i.e.,

what are the odds of the population data occurring outside the sample data? This is

used in political polling when projecting a winner in an election. With a small

percentage of the vote cast (sample) certain statistical extrapolations can be made to

indicate if this is reflective of the voting public (population), answering the question

“What are the odds the other candidate can still catch the leading candidate?” This also

speaks to the assurance one has that their descriptive statistics are accurate. It becomes a

matter of confidence. How confident are you that your study of the sample is an accurate

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depiction of the population? Las Vegas “odds-makers” are the heir apparent to this

form of statistics, since it began with a gambling question.

In the mid-1600s a professional gambler named Chevalier de Mere made fortune.

He would bet unsuspecting patrons that in 4 rolls of a die he could get a six at least

once. He was so successful at the game that soon people refused to play him. He then

challenged them that he could roll two sixes in 24 rolls of the die . . . he failed.

Confused, he contacted Blaise Pascal – famous mathematician. He corresponded with a

friend, Pierre de Fermat, and they developed the first successful theory of probability . .

. inferential statistics!2 This may be the only beneficial development from the gambling

industry!

Correlation Statistics

When the temperature rises, so does the red line in a

thermometer. As it cools, the red line lowers. There is an obvious

relationship between the red line and the temperature. However, if

someone had never seen a thermometer before, they could incorrectly

conclude, “Amazing, if the red line drops, the temperature lowers; and if it goes up, the

temperature rises!” Correlation statistics is a special form of descriptive statistics in

which the relationship between two or more variable relate to one another. Correlation

can not only determine the presence of a relationship, but the nature of the relationship

as well. “Is there a connection between small group participation and involvement in

the congregation’s ministry?” This is a question that correlation statistics can answer.

In its most basic form, only the fact of the relationship can be demonstrated, not the form

of the relationship, e.g. causation. More advanced correlation statistics can determine

not only the existence of a relationship, but the event of causation. Correlation statics

are in part based on Inferential statistics, since it is dealing with a sample and

explaining the probability of an event, i.e. if this happens to X, then Y occurs this much.

Variables?

A variable is the item or items being analyzed. If I want to see the correlation

between a students grade point average and their score on a standardized test (such as

SAT, ACT, or GRE), then I’m studying the relationship between two variables.

2 Cf. Allan G. Bluman (1995), Elementary Statistics, 2nd Edition (Chicago: Irwin), 13.

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Variables come in two different types: Categorical are those that are non-numerical,

such as gender, which has two categories male and female. Numerical variables are

counted or measured. Discrete numerical variables are counted in whole numbers, e.g. 1,

2, 3, 4; like asking how many times someone attended worship annually. Continuous

numerical variables are continuous because they are not simply counted, but are

measured, i.e. using decimals, and hence are continuous; e.g., the distance a household

is from your church building, 5.239 miles. You could say discrete is a count, continuous is

an amount. The type of variable does appropriate statistical formula and the way in

which data is presented (Section 6).

Common Problem: Mismatching!

As Table 2.1 illustrates, the appropriate use of statistics requires alignment. The

question being asked requires the application of the appropriate type of statistics.

Different types of statistics have different formulas associated with them. Finally, the

outcomes of the different statistical formulas lend themselves to different analyses of

the data. In short, mismatching creates an irreconcilable error to occur in research. For

example, if statisticians hear the phrase “Chi-squared,” they know that inferential

statistics are involved; whereas if someone mentions Pearson r, then correlation

statistics are being discussed. [If you are slightly panicking right now; fear not, these

will be explained later in the paper, and all these functions are calculated by Excel. For

now, just realize that all statistics are not alike.] Likewise, if inferential statistics are

being applied, then one can assume that hypothesis testing or sample reliability are

involved. Similarly, if correlation statistics are being used, one can assume that the

question involves the relationship of two variables. Table 2.1, as well as Figure 4.1 and

5.1, are designed to maintain statistical alignment in research design.

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Section 3

Descriptive Statistics

What’s going on here?

You have a large set of numbers . . . how do you

describe them? Descriptive statistics are designed to

provide an accurate overview of any set of numbers. Like a

photograph, they capture certain elements of the scene.

Like the photo to the left, you could say, “It has palm trees,

a beach, an ocean, and mountains in the distance.” While

there may be more the photo, such as waves in the ocean, or mountains closer than

others in the distance, the descriptive given is enough to identify the photo and

accurately describe the contents. Descriptive statistics has several standard methods of

describing a set of numbers. It is not designed to project or capture an image beyond

the limits of the frame, or explain the relationship between items in the photo. Photos

capture one moment in time within the limited scope of the lens. That is descriptive

statistics.

Descriptive Statistics Computations

Mean: The technical term for “average,” the balancing point of all the data. It is

derived by adding all the values in a data set and dividing by the number of values.

This is designed to identify the center of the data, i.e. central tendency.

Median: The middle value when all the values in a data set are arranged lowest to

highest. This is designed to identify the center of the data, i.e. central tendency.

Mode: The value in a data set that occurs most frequently.

Range: The difference between the lowest and highest number in a data set. This is

designed to demonstrate the spread of values in a data set, the variance.

Quartiles: The three values that split a data set into four equal parts, or quarters.

This is designed to summarize large data sets into 25th, 50th, and 75th percentiles, i.e.

quarters. Note: standardized educational testing uses the quartile system.

o Q1, the first quartile, 25%, means that a quarter of the values in the data set are

smaller than this value and 75% are larger

o Q2, the second quartile, 50%, means that half of the values in the data set are smaller

than this value and half are larger.

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o Q3, the third quartile, means that 75% of the values in the data set are smaller than

this value and 25% are larger.

Whisker-Box Plot: It is like a graphic representation of quartiles. It is a test of

“skewness,” i.e. the relation of the mean and median in a data set (See Figure 3.1).

o Symmetrical Shape: When the mean and median are the same

o Left-Skewed Shape: When the mean is less than the median, and hence more

values are to the left of the mean.

o Right-Skewed Shape: when the mean is more than the median, and hence more

values are to the right of the mean.

o NOTE: This is critical since inferential statistics assumes that data has a

symmetrical shape, or bell curve.

Figure 3.1: Symmetric, Left, and Right Skewed Data Sets

Z-score: The difference between a value and the mean, divided by the standard

deviation. This is designed to identify the spread of data from the mean, the variance. Z-

score is a score; meaning it is used to assess variance. A Z-score of +/- 3 identifies

that that value is an extreme value, far from the mean.

Standard Deviation: The measure of variation of a set of data from the mean, like the

width of the mean. This is designed to demonstrate the spread of data from the mean of the

data set.

ILLUSTRATION

You are an instructor in a seminary. You give a midterm exam to a class of 20

students. The following are the scores on the midterm (the data set), arranged smallest

to largest:

0

1

2

3

4

5

6

Symmetric Left Right

Mean Mean Mean

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58 59 63 68 74 77 83 85 87 88

88 88 90 90 91 92 95 96 97 99

At lunch, a colleague asked, “How did your student do on the midterm?” Rather

than rattling off the grade book, you could simply respond as follows:

Mean: 83.4

Median: 88.5 (since it is an even numbered data set, 20 values, the median is

between the 10th and 11th value).

Mode: 88 (That value occurs three times in the data set, more than any other

value)

Range: 41 points (the highest value – the lowest value, i.e. 99-58 = 41)

Quartiles: Q1 = 76.25

Q2 = 88

Q3 = 91.25

Skewness: 0.931 (using Microsoft Excel, this figure was provided. Since a value of

0 would indicate a symmetrical skew, and this is “close,” i.e. it is still a zero-

point-something, then the data is almost symmetrical, maybe only slightly

skewed!

Z-score: Since the Z-score for the lowest test was -2.0 and the Z-score for the

highest was +1.23; neither being outside the +/- 3 range, none of the scores are

considered “extreme.”

Standard Deviation: 12.65 points, meaning most of the grades were between 96.05

(the mean + the standard deviation) and 70.75 (the mean – the standard

deviation).

This is probably more information than your colleague requested, required, or

even expected, but it does provide an accurate depiction of the class’ performance on

the midterm exam!

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Section 4

Inferential Statistics

How sure am I that my description is accurate?

Inferential statistics can be described in a variety of

ways, but perhaps the most common phrase is, “What

are the odds of that happening?” Inferential statistics is

the mathematical basis of gambling, or more

specifically probability. However, for our purposes, the

basic description for our purposes is to discuss the

difference between sets of data. It is used in research to determine the level of confidence

one can have generalizing conclusion about the population from a sample. “How

confident can I be that the sample’s data is an accurate reflection of the population in

general?” This is the task of inferential statistics. We can assume that the data drawn from

a sample of a population will accurately reflect the actual population; but that’s an

assumption! Inferential statistics serves to validate more objectively the accuracy of the

sample’s data in relation to the population. Rather than having to say, “I feel confident .

. .” or “Well, I hope it’s accurate!”, a statistician can say, “I’m 90% confident that the

sample data accurately reflects the population.”

Inferential Statistic Calculations

Hypothesis Testing refers to a set of methods used to make inferences about

expected or hypothesized values between a sample and population. What methods

(plural) are available for testing hypotheses?

p-value approach: Given the null hypothesis is true, the p-value tests for extreme

values in the sample. You reject the null hypothesis if the p-value is less than α, you

do not reject the null hypothesis is the p-value is more than α. Hence the phrase, “If

the p-value is low, then the null hypothesis must go.”

o α , also known as “level of significance, refers to the odds of a Type 1 error

occurring in a hypothesis test. It should be measured at .05 to insure a Type 1

error does not occur.

Z-test (not Z score): What level of confidence do you have that a given set of data is

normally distributed and that a given value falls into a predictable pattern, not in

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the extreme? This is the Z-test or Z-value. Typically, 95% is the level of certainty

used in research. This corresponds to a Z-value of +/- 1.96. If a test statistic is

greater than 1.96, you reject the null hypothesis. If you lower the level of certainty,

this may change . . . but

Inferential Statistics Flowchart3

Figure 4.1

Figure 4.1

DESCRIPTIONS

Wilcoxin Matched Pairs t-Test: It is like the Matched samples t-Test. See below

3 Adapted from Dr. Rick Yount, (2006). “Research Design and Statistical Analysis in

Christian Ministry,” 4th Edition. (self published, Southwestern Baptist Theological

Seminary, Fort Worth, Texas), pp. 5-3, and subsequent material from pp. 5-4 to 5-7.

Group

Differences

Ordinal Interval

2 Groups

3+ Groups 1 Group

3+ Groups

Wilcoxin

Matched

Pairs T-test

Mann-

Whitney

U-test

Wilcoxin

Rank-Sum

test

Kruskal-

Wallis H

test

One-sample

z-test

Sample &

Population

mean known;

n>30

One-sample

t-test

σ unknown

Independent

Samples t-test

2 Independent

Groups

Matched

Samples t-test

2 matched

groups

2 Groups

One-way

ANOVA

1 ind. var., 1

dep. var. – ind.

groups

Factorial

ANOVA

2+ ind. var., 1

dep. var. – ind.

groups

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Mann-Whitney U Test: Compares two independent samples; e.g. “Did learning, as

measured by the number correct on a quiz, occur faster for Class 1 or Class 2?” It is like

the Independent Samples t-Test.

Wilcox Rank Sum: Compares the magnitude and direction of differences between two

groups, e.g. “Is Bible college twice as effective as no Bible college experience for helping

develop writing skills?” It is like the Independent Samples t-Test.

Kruskal-Wallis H Test: A form of ANOVA that compares the difference between two or

more independent samples; e.g. How do rankings of associate deans differ between

four academic fields?” Like the one-way ANOVA.

One-sample z-test: Is data from one sample significantly different from its population?

If the sample is > than 30, use this test

One-sample t-test: Is data from one sample significantly different from its population? If

the sample is < than 30, use this test. See below

For example: You know the average age of pastors in the SBC. You collect

information from a single sample of SBC pastors with seminary educations. Is

there a significant difference in the average age of the sample and the

population?

Independent Samples t-Test: Like the ones above, this test computes whether data from

two independently randomly selected samples is significantly different. See below

Matched Samples t-Test: This test computes whether data from two groups of paired

subjects (e.g. husbands and wives; elders and deacons) samples is significantly

different. See below

One-way ANOVA (Analysis of Variance): Also known as a F-test, it tests for difference

between two or more means on one dimension, e.g. How do rankings of associate deans

differ between four academic fields?”

Factorial/Two-way ANOVA (Analysis of Variance): tests for difference between two or

more independent samples on more than one dimension; e.g. How do rankings of

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associate deans differ between four academic fields and gender?” It measures the

interaction among the independent variables.

t-Test, but which one?

When you are testing for differences between groups, a variety of t Tests are available.

How do you know which one to use?

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Figure 4.24

4 Adapted from Neil J. Salkind (2008), Statistics for People Who Think They Hate Statistics

(Los Angeles: Sage Publications), 190.

Same

Participants

YES NO

2 Groups

3+ Groups 3+ Groups

t-test for

dependent

samples

Related

measures

of analysis

of variance

t-test for

independent

samples

2 Groups

Simple

Analysis of

Variance

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Hypothesis Testing Made Easy!

Figure 4.3

State a Hypothesis

(Null & Alternative)

Set the Level of

Significance (α)

(typically .05)

Select the Appropriate Test

Mean/Variance, z-Test, t-Test, X2, ANOVA

Calculate p-value &

compare to α

Reject or Accept the Null Hypothesis!

General Rule: If p is low, then the

hypothesis must go.

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Section 5

Correlation Statistics

How does X influence Y?

“I wonder if there is a relationship between the temperature in

my dorm room and the red liquid in the thermometer? What

might be that relationship?” Correlation statistics is used to

determine the existence, strength, and direction of variables in a

study, especially similarities among variables. “Yes, there is a

relationship between the temperature in my dorm room and the red liquid in the

thermometer. When temperature rises, the red liquid rises in direct relation to the

temperature, and this is very strong relationship.” Correlation statistics are sometimes

called coefficient of similarity or just association.

Different tests are used depending on the type of variable:

Categorical or Nominal: one that has two or more categories, but there is no

intrinsic ordering to the categories, e.g gender has two categories (male and

female) or hair color having more than two categories (blonde, brown, brunette,

red). Neither of these categories have an order highest to lowest.

Two Categories: Spearman rho ( ) and/or Kendall’s tau ( )

Three or More Categories: Kendall’s W

Ordinal: Like a categorical or nominal variable, except there is an obvious

ordering of the variables, e.g. economic status with three categories (low,

medium and high) or educational experience with levels such as elementary

school graduate, high school graduate, some university and university graduate.

In both instances, the spacing between the values may not be the same across the

levels of the variables.

One Categories: Chi-squared (χ2), “Goodness of Fit”

Two Categories: Chi-squared (χ2), “Test of Independence”

Interval: Like an ordinal variable, except that the intervals between the values are

equally spaced, e.g. measuring economic status in increments of $10,000, the

space between the variables is equal.

Two Categories: Pearson’s r and Linear Regression

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Three Categories: Multiple Regression

Specific types of tests are tied to specific types of variables. Mismatch the variable and/or

test, bad data!

Correlation Flow Chart5

Figure 5.1

Figure 5.1

DESCRIPTIONS

Spearman rho (ρ): Computes correlation between ranks (used when at least 10 or more

pares of rankings are available) given by two groups; e.g. “What is the correlation

between rank in the senior year of college and rank during the first year of seminary?”

5 Adapted from Dr. Rick Yount, (2006). “Research Design and Statistical Analysis in

Christian Ministry,” 4th Edition. (self published, Southwestern Baptist Theological

Seminary, Fort Worth, Texas), p. 5-3, and subsequent material from pages 5-4 to 5-7.

Relationships/

Similarities

Categorical Ordinal Interval

2 Ranks

3+ Ranks

1

Variable

2

Variables

2

Variables

3+

Variables

Spearman

rho (ρ)

Kendall’s

tau (τ)

Kendall’s

W

Chi-square

Goodness

of Fit

Chi-square

Test of

Indepen-

dence

Contingency

Coefficient;

Cramer’s Phi

Pearson’s r

Simple

Linear

Regression

Multiple

Regression

P a g e | 21

Kendall’s tau (τ): Similar to Spearman rho, but used when less than 10 ranks are

available given by two groups; e.g. two church staff members’ ranking a list of seven

characteristics about church health, this could compute the degree of agreement

between the rankings.

Kendall’s W (also known as Kendall’s Coefficient of Concordance): Similar to the

Spearman rho and Kendall’s tau, it measures the degree of agreement in ranking from

more than two groups, 3+. e.g. five church staff members’ ranking a list of seven

characteristics about church health, this could compute the degree of agreement

between the rankings.

Chi Square (χ2): Determines if the number of occurrences across categories is random;

e.g. “Did coffee, hot chocolate, and hot tea sell an equal number of cups during the last

week?”

Chi Square Goodness of Fit: Compares actual categorical counts with expected

categorical counts, e.g. did actual gender enrollment match what was expected?

How good did the expectation fit the actual?

Chi Squared Test of Independence: Compares two categorical variables to

determine if any relationship exists between them, i.e. are they independent

variables.

Pearson r (or Pearson’s Product Moment Correlation Coefficient): Directly measures the

degree of relationship between two interval variables.

Simple Linear Regression: Computes an equation of a line which allow researchers to

predict one interval variable from another, e.g., “If x . . . then y.”

Multiple Regression: A statistical procedure where several interval variables (3+) are

used to predict one.

t Test, but which one?

When you are testing for relationships or similarities between groups, a variety of t

Tests are available. How do you know which one to use?

P a g e | 22

Figure 5.26

6 Adapted from Neil J. Salkind (2008), Statistics for People Who Think They Hate Statistics (Los Angeles: Sage

Publications), 190.

How many

variables?

2 Groups

3+ Groups

t-test for significance

of the correlation

coefficient

Regression,

factor

analysis

P a g e | 23

Section 6

What to Watch Out For

Common Errors, Mistakes, Misfortunes, and Resources of

Statistics (& Quantitative Research)

Appropriate Presentations

If the variable is categorical . . .

Determine 1-2 variables to present

If one, use summary chart, or a bar, pie, or pareto chart

If two, 2-way cross table

If the variable is numerical . . .

Determine 1-2 variables to present

If one, use frequency and percentage distribution, histogram or a dot scale

If two, determine if time order is important:

o If yes, time-series plot

o If not, use a scatter plot

Resources for Statistical Work7

www.statistics.com

http://www.psychstat.missouristate.edu/scripts/dws148f/statisticsresourcesmain.asp

http://www.stat.ucle.edu/calculators/

http://www.Anselm.edu/homepage/jpitocch/biostatshist.html -- history of statistics

http://www.anu.edu.au/nceph/surfstat/surfstathome/surfstat.html

http://www.davidmlane.com/hyperstat/index.html -- tutorials!

http://www.lib.umich.edu/govdocs/stats.html

http://mathforum.org/workshops/sum96/data.collections/datalibrary/data.set6.html

http://www.stat.ufl.edu/vlib/statistics.html

http://noppa5.pc.helsinki.fip/links.html

Survey Dilemmas8 Ill-defined Population

7 Neil J. Salkind (2008), Statistics for People Who Think They Hate Statistics (Los Angeles:

Sage Publications), Chapter 19. 8 Adapted from Deborah Rumsey (2003), Statistics for Dummies (Hoboken, New Jersey:

Wiley Publishing), Chapter 20.

P a g e | 24

Mismatched Sample and Population

Sample wasn’t randomly selected

Sample wasn’t large enough

Insufficient response to requests

Inappropriate form of survey

Misworded survey items (statements or questions)

Timing of the Study

Inadequate training for research assistants

Survey items didn’t relate to the research questions

Avoiding Erroneous Statistical Conclusions9

Statistics don’t prove anything.

Conclusions cannot be based on statistically insignificant data

Correlation does not mean causation

Assuming a normal distribution without demonstrating a normal distribution.

Partial reporting of the findings

Assuming a larger sample size is better and solves all problems

Intentional omission of unexpected findings

Misapplication of results beyond the population.

Conclusions based on non-random sample

Selected vs. Responded

9 Adapted from Deborah Rumsey (2007), Intermediate Statistics for Dummies (Hoboken,

New Jersey: Wiley Publishing), Chapter 21.

P a g e | 25

Bibliography

Levine, David M. and David F. Stephan (2005). Even You Can Learn Statistics. Upper

Saddle River, New Jersey: Pearson/Prentice Hall.

Pyrczak, Fred (2006). Making Sense of Statistics: A Conceptual Overview, 4th Edition.

Glendale, California: Pyrczak Publishing.

Rumsey, Deborah (2003). Statistics for Dummies. Hoboken, New Jersey: Wiley

Publishing.

________ (2007). Intermediate Statistics for Dummies. Hoboken, New Jersey: Wiley

Publishing.

Salkind, Neil J. (2008). Statistics for People Who (Think They) Hate Statistics, 3rd Edition.

Los Angeles: Sage Publications.

Yount, Rick (2006). “Research Design and Statistical Analysis in Christian Ministry,” 4th

Edition. Fort Worth, Texas: Southwest Baptist Theological Seminary.