Measurement Theory in Marketing Research

Measurement What is measurement?  Assignment of numerals to objects to represent quantities of attributes Don’t measure the object -- measure attributes of the object  Don’t measure a person -- measure their weight, height, social class, GPA, etc. Definition does not suggest how to measure the attributes

Measurement Measurement Scales  Four types -- NOIR  Nominal -- Number is used for identification purposes Jon Laczniak is number 5 Matt Laczniak is number 9  Numbers reflect nothing -- just used to identify the person

Measurement  Ordinal -- Number is used to reflect order Jon Laczniak is in 7th grade at Ames Middle School; Ethan Constant is in 3 rd Grade  Jon is in a “higher” grade  How much higher?  Cannot really tell (depends on programs, etc.)  No true 0 and differences between grades is not constant  Interval -- Number reflects “intervals” between attributes Matt Laczniak scored 96 on his soccer skills test; Jon Laczniak scored a 32  Matt scored 64 points higher than Jon!  Is he three times as good?  Can we really say that someone has “0” soccer skills?

Measurement Ratio -- Number has an absolute 0  Andy Laczniak is 22 years old; Jon Laczniak is 11 years old Andy is twice as old as Jon Age has a real (and interpretable) 0

Measurement X O = X T + (E S + E R )  X O = Observed score for some construct  X T = True score for some construct  E S = Systematic Error  E R = Random Error

Measurement Objective in research -- X O = X T  When this happens, the measure is valid If X R = 0; X O = X T + E S  Measure is reliable  Free of random error

Measurement Reliability -- instrument measures the same concept every time it is used (X O = X T + E S ) Validity -- instrument measures what it intends to measure (X O = X T ) Given that X O = X T + E S suggests X O is free of random error -- this indicates reliability  Reliability is a necessary, but not sufficient indicator of validity

Measurement Assessing Reliability (X O = X T + E S )  Consistent responses across time (test/retest reliability)  Internally consistent -- all aspects of the measure work together Multiple measures (of the same concept) are needed  Laczniak Yogurt is:  Good/Bad; Favorable/Unfavorable; Positive/Negative Coefficient alpha = k (mean inter-item correlation)/{1 +[ (k-1) (mean inter-item correlation)]}  Here – 3 items are used to measure attitude  Need to calculate correlations between each item (3) and then compute the mean

Measurement Calculation of coefficient alpha (  ) k (mean inter-item correlation)/1 +[ (k-1) (mean inter-item correlation)]  Where k = number of items used to measure a concept Thus, if one item is used  Mean correlation = 0  Thus,  = 0  Single item measures have reliability = 0 Example  K = 3  Mean inter-item correlation =.80   = ?? Rules of Thumb   =.70 (for new/exploratory measures of concepts)   =.85 (for measures that have previously been shown to be reliable)

Measurement Indicators of Validity (X O = X T )  Face validity Measure “looks” like it should Best to have others (“expert judges” determine this)  Discriminant Validity Measure does not measure some other concept Correlation with measure of other concept is very low  Convergent Validity Measure corresponds to other measures of this concept Correlation with other measures of this concept is high

An Example of Measurement Ranking versus Rating  Rank -- respondent orders the brands according to their attitude (Ordinal Scale)  Rating -- respondent rates each brand on a similar scale (Interval Scale) ***

An Example of Measurement Likert Scales -- scales in which respondents indicate their degree of (dis) agreement with statements about the object  Generate large number of statements about the attitude object (e.g, “Professor Laczniak is an exceptional instructor”)  Classify the statements a priori as (un) favorable

An Example of Measurement Likert Scales (cont’d)  Determine a method of scoring (3-point versus 5-point versus 7-point or more; use a midpoint or not – 4-point) Agree, Neutral, Disagree Strongly Agree, Agree, Neutral, Disagree, Strongly Disagree  Purify the scale by eliminating ambiguous items (through pre-tests) If an item makes the alpha coefficient lower – drop it  Use the scale Has a midpoint (can say if mean response is above/below it) Is interval scaled -- can make mean comparisons Must develop your own norms (midpoints do not always apply)

An Example of Measurement Semantic Differential -- uses a series of 7-point gradations with bipolar adjectives that anchor the beginning and end of each scale Most commonly used -- “My attitude toward the Compaq brand is:” Good ___:___:___:___:___:___:___ Bad Positive ___:___:___:___:___:___:___ Negative Favorable ___:___:___:___:___:___:___ Unfavorable

Measurement Internal versus External Validity  Internal Validity – ability to demonstrate that the an observed effect is due to the experimental manipulation (Lab Setting)  External Validity – ability to generalize the results of an experiment beyond the experimental subjects (Real World) Internally valid studies are typically not “real” Externally valid studies typically have less controls  Ideally, we follow a lab study with one in the real world