Measurement

1. Measurement Chapter 8 Cooper and Schindler

2. 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

3. Characteristics of Measurement Gender Styling Characteristics A B C D E A B C D E Desirability of styling to show attendees A-E Gender of show attendees A-E Empirical Observations Assign 5 if Very Desirable 4 if Desirable 3 if neither 2 if undesirable 1 if Very Undesirable Mapping Rule Assign “M” if male “F” if female 1 2 4 3 5 (1 through 5) M F Symbol

4. What Is Measured? (I) • 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

5. What Is Measured? (II) • Age, Years of experience, Number of calls per week • It is not easy to measure properties • 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

6. Scale Classifications • 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)

7. 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

8. 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

9. 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

10. Ordinal Scales • 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

11. 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)

12. 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

13. Sources of Measurement Differences • The respondent as an error source • Situation factors • The measurer as an error source • Instrument as an error source

14. Sound Measurement • 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

15. 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

16. 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

17. 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

18. 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 • 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

19. 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

20. 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

21. 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

22. 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

23. 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