Measuring and Scaling of Quantitative Data

Prof. Dr. Khalid MahmoodUniversity of the Punjab

Lahore-PAKISTAN

Agenda

What are measuring and scaling? Levels of measurementProcess of measurementMethods of scalingTypes of scalesReliability and validity of scales

What are measuring and scaling?

Measurement: The process of describing some property of a phenomenon by assigning numbers.

Scale: A type of composite measure composed of several items that have a logical or empirical structure among them. It allows to measure the intensity or direction of a construct by aligning the responses on a continuum.

“If a thing exists, it exists in some amount; and if it exists in some amount, it can be measured.”

–E. L. Thorndike (1914)

Levels of measurement

NominalOrdinalIntervalRatio

Nominal A categorical variable, also called a nominal

variable, is for mutual exclusive, but not ordered, categories.

Nominal scales are mere codes assigned to objects as labels, they are not measurements.

Not a measure of quantity. Measures identity and difference. People either belong to a group or they do not.

Sometimes numbers are used to designate category membership.

Examples: Gender, eye color, marital status

Ordinal

This scale has the ability to rank the individual attributes of two items in same group but unit of measurement is not available in this scale, like student A is taller than student B but their actual heights are not available.

Designates an ordering: greater than, less than.

Does not assume that the intervals between numbers are equal.

Interval

Classifies data into groups or categories Designates an equal-interval ordering The difference in temperature between 20 degrees

Fo and 25 degrees Fo is the same as the difference between 76 degrees Fo and 81 degrees Fo

Zero point on the interval scale is arbitrary zero, it is not the true zero point

Common IQ tests are assumed to be interval measures

Ratio

This is the highest level of measurement and has the properties of other three levels; coupled with fixed origin or zero point.

Measurements of heights of students in a class (zero means complete lack of height).

Someone 6 ft tall is twice as tall as someone 3 feet tall.

Heart beats per minute has a very natural zero point. Zero means no heart beats.

Process of measurement

Define concepts to be measured Define attributes of the concepts Select level of measurement (data type) Generate items/questions

Wording Response format

Layout and design questionnaire Pretest and refine

Methods of scaling

Rating scales Have several response categories and

are used to obtain responses with regard to the object, event, or person studied.

Ranking scales Make comparisons between or among

objects, events, persons and obtain the preferred choices and ranking among them.

Types of scales

Likert scale Semantic differential scale Stapel scale Graphic rating scale Thurstone scale Guttman scale Paired comparison scale Forced choice Comparative scale

Likert scale Is designed to examine how strongly subjects agree or

disagree with statements on a 5-point scale.

Semantic differential scale Several bipolar attributes are identified at the

extremes of the scale, and respondents are asked to indicate their attitudes.

Stapel scale

This scale simultaneously measure both the direction and intensity of the attitude toward the items under study.

It is a slight modification of semantic differential scale.

The scale consists of a single adjective in the middle of positive and negative numbers

Stapel scale

Graphic rating scale

A graphical representation helps the respondents to indicate their answers to particular question by placing a mark at the appropriate point on the line.

Thurstone scale This technique assesses the extent of agreement

among a group of judges about the proposed items for a scale.

For example, one might ask a group of persons to judge how closely 25 different items come to measuring self-esteem. Then, one might select the 10 items that received the highest average scores for having content validity with self-esteem.

It can help find the best questions to ask to measure an abstract concept.

It does not specify how a question or set of questions should be formatted on a questionnaire.

Guttman scale Who agrees with an item will also agree with all other

items expressing a less extreme position Using a series of statements to reflect the strength of

attitudes

-

“I think the following contains pornographic materials.”Subject

Adult movies rated XXX

A[Yes

]

B[Yes]

C[Yes]

Scale Value

4

Playboy magazine [Yes]

[Yes]

[No]

3

Lingerie ads [Yes]

[No]

[No]

2

New York Times [No] [No]

[No]

1

Paired comparison scale

The respondents are asked to choose between two objects at a time.

Forced choice

Enables respondents to rank objects relative to one another, among the alternatives provided.

Comparative scale

Provides a benchmark or a point of reference to assess attitudes toward the current object, event, or situation under study.

Reliability of scale

Indicates the extent to which it is without bias (error free) and hence ensures consistent measurement across time and across the various items in the instrument.

Types of reliability

Stability of measures Test-retest reliability Parallel-form reliability

Internal consistency of measures Inter-item consistency reliability

Cronbach’s alpha Split-half reliability

Validity of scale

Ensures the ability of a scale to indeed measure the concept we want to measure and not something else.

Content validity Criterion related validity Construct validity

Content validity

Ensures that the measure includes an adequate and representative set of items that tap the concept. A panel of judges

Criterion related validity

Is established when the measure differentiates individuals on a criterion it is expected to predict.

Concurrent validity: established when the scale differentiates individuals who are known to be different

Predictive validity: indicates the ability of measuring instrument to differentiate among individuals with reference to future criterion

Construct validity

Testifies to how well the results obtained from the use of the measure fit the theories around which the test is designed. Convergent validity: established when the scores

obtained with two different instruments measuring the same concept are highly correlated

Discriminant validity: established when, based on theory, two variables are predicted to be uncorrelated, and the scores obtained by measuring them are indeed empirically found to be so

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