Measurement Scales

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Measurement

• Consist of assigning numbers to empirical events in compliance with a set of rules

• The definition implies that measurement is a three-part process

– Selecting observable empirical events

– Using numbers or symbols to represent aspects of the events

– Applying a mapping rule to connect the observation to the symbol

• Example

– Studying people who attend an auto show where all of the year’s new models are on

display

• Gender

• Styling characteristics

What is measured ?

• Concepts

– Objects

• Include the things of ordinary experience, such as tables, people, books and

automobiles

• Also include things that are not as concrete, such as genes, attitudes, neutrons

and peer-group pressures

– Properties

• Are the characteristics of the objects

• Physical properties

• Psychological properties

• Social properties

• Researchers measure indicants of the properties of objects

– Age, Years of experience, Number of calls per week

• It is not easy to measure properties

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– Motivation to succeed, ability to stand stress, problem-solving ability, and

persuasiveness

– There is often disagreement about how to operationalize the indicants

• Not only is it a challenge to measure such constructs, but a study’s quality depends on what

measures are selected or constructed, and how they fit the circumstances

Scale Classification

• Employ the real numbers systems

• The most accepted basis for scaling has three characteristics

– Number are ordered (Order)

– Differences between numbers are ordered (Distance)

– The number series has a unique origin indicated by the number zero (Origin)

Measurement Scales

• Nominal

– No order, or origin

– Determination of equality

• Ordinal

– Order but no distance or unique origin

– Determination of greater or lesser values

• Interval

– Both order and distance but no unique origin

– Determination of equality of intervals or differences

• Ratio

– Order, distance, and unique origin

– Determination of equality of ratios

Nominal Scales

• Partition a set into categories that are mutually exclusive and collectively exhaustive

• Counting is the only arithmetic operation

– Only labels and have no quantitative value

• No order or distance relationship and have no arithmetic origin

• No general used measure of dispersion

• Several tests for statistical significance may be utilized

– Chi-square test

– For measures of association, phi, lambda, or other measure may be appropriate

Ordinal Scales

• Include the characteristics of the nominal scale plus an indicator of order

• Ordinal scales are possible if the transitivity postulate is fulfilled.

• An extension of the ordinal concept occurs when more than one property is of interest

– Add and average ranks is technically incorrect

– Use a multidimensional scale

• Have another difficulty when combining the rankings of several respondents

– Convert the ordinal scale into an interval scale

– Thurstone’s Law of Comparative Judgment

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• Examples of ordinal scales include opinion and preference scales

– Paired -comparison techniques

• Ordinal scales have only a rank meaning

• Statistical measures

– Central tendency

• median

– Dispersion

• Percentile or quartile

– Correlation

• Rank-order methods

– Statistical significance

• Nonparametric methods

Interval Scales

• Has the powers of nominal and ordinal plus one additional strength

– Incorporates the concept of equality of interval

• Calendar time is interval scales

– Zero time and zero degree(Centigrade and Fahrenheit) are arbitrary origin

• Many attitude scales are presumed to be interval

– Thurstone’s differential scale was an early effort to develop such a scale

• Statistical measures

– Central tendency (Arithmetic mean)

– Dispersion (Standard deviation)

– others (Product moment correlation, t-tests, and F-tests)

Ratio Scales

• Incorporate all of the powers of the previous ones plus the provision for absolute zero or origin

• Represent the actual amounts of a variable

• Examples are weight, height, distance, and area

• In behavioral sciences, few situations satisfy the requirement of the ratio scale(Psychophysics

offering some exceptions)

• In business research, we find ratio scale in many areas (money values, population counts,

distances)

• Statistical measures

– All statistical mentioned up to this point

– Multiplication and division

– Geometric mean, coefficients of variation

Sources of Measurement Differences

• The respondent as an error source

• Situation factors

• The measurer as an error source

• Instrument as an error source

Sound Measurement

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• Validity

– Content validity

– Criterion-related validity (Concurrent validity, Predictive validity)

– Construct validity

• Reliability

– Stability (Test-retest)

– Equivalence (Parallel forms)

– Internal consistency (Split-half, KR-20, Cronbach’s alpha)

• Practicality

– Economy

– Convenience

– Interpretability

Criteria for Evaluating a Measurement Tool

• Validity

– Refer to the extent to which a test measures what we actually wish to measure

• Reliability

– Has to do with the accuracy and precision of a measurement procedure

• Practicality

– Is concerned with a wide range of factors of economy, convenience, and interpretability

Validity

• Internal and external

• Research Instrument internal validity

– Measure what it is purported to measure

– Does the instrument really measure what its designer claims it does?

• Three major forms

– Content validity

– Criterion-related validity

• Concurrent validity

• Predictive validity

– Construct validity

Content Validity

• The extent to which it provides adequate coverage of the topic under study

• Determination of content validity is judgmental and can be approached in several ways

– Through a careful definition of the topic

– Use a panel of persons to judge

Criteria-Related Validity

• reflects the success of measures used for prediction or estimation

– Predict an outcome

– Estimate the existence of a current behavior or condition

• Predictive and concurrent validity differ in time perspective

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– An opinion questionnaire that correctly forecasts the outcome of a union election has

predictive validity

– An observational methods that correctly categorizes families by current income class

has concurrent validity

• Any criteria measure must be judged in terms of four qualities: relevance, freedom from bias,

reliability, availability

Construct Validity

• One may wish to measure or infer the presence of abstract characteristics for which no

empirical validation seems possible

– Attitude scales

– Aptitude tests

– Personality tests

• Example

– Measuring the effects of ceremony on organizational culture

– Ceremony was operationally defined would have to correspond to an empirically

grounded theory

• Convergent validity

• Discriminant validity

Reliability

• A measure is reliable to the degree that it supplies consistent results

• Reliability is a contributor to validity and is a necessary but not sufficient condition for validity

• Reliability is concerned with estimates of the degree to which a measurement is free of random

or unstable error

Stability

• A measure is said to be stable if you can secure consistent results with repeated measurements

of the same person with the same instrument

• Test-retest

Equivalence

• Considers how much error may be introduced by different investigators (in observation) or

different samples of items being studied (in questioning or scales)

• Equivalence is concerned with variations at one point in time among observers and samples of

items

• Interrater reliability may be used to correlate the observations or scores of the judges and

render an index of how consistent their ratings are

Internal consistency

• Use only one administration of an instrument or test to assess consistency or homogeneity

among the items

– Split-half techniques

• Spearman-Brown correction formula

• The test splitting may influence the internal consistency coefficient

– Kuder-Richardson Formula 20

– Cronbach’s Coefficient Alpha