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1
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