Vaughn C. Judd, Auburn University Montgomery
Analyzing The Price–Quality Relationship
The relationship between product price and quality is more relevant to students when they
analyze it using third-party data. Food product ratings in Cook’s Illustrated magazine provide the
data for the analyses. Consumer Reports, however, can be used as a data source if Cook’s
Illustrated is not readily available. The Spearman rank correlation coefficient, an easy statistic to
calculate in class with a hand-held calculator, is used to measure the relationship.
An Example of the Process
Step 1: Students are grouped in teams of two or three. Each team is given a reprint of a different
food review from Cook’s Illustrated magazine and a worksheet that is equivalent in form to
Table 1, but with only the column headings.
Step 2: The example, Table 1, is based on ratings of six brands of canned red kidney beans.
Students list the brands in column 1 and the rank order of quality in column 2—the best quality
being ranked number one. Although there are no ties in quality ranks in this example, brands are
sometimes tied.
Step 3: Students then list the price and volume of each brand in column 3. Since the cans contain
different volumes, the prices from column 3 are converted to per ounce equivalents in column 4.
The prices shown in column 4 are ranked from highest to lowest (1 = highest) in column 5. Note
that there are two brands with identical prices—at $.030/ounce. Using the midrank method for
handling ties, these brands are each ranked 5.5.
Step 4: Students next calculate the coefficient of correlation between the quality and price
rankings. First, they complete the d (difference) column by subtracting the x rank from the y rank
for each brand, then the d2 column by squaring the values in the d column and summing them up.
Finally, the coefficient of correlation is calculated.
Step 5: Each group is asked to draw conclusions regarding the relationship between price and
quality for the brands analyzed and to report the conclusions to the class. The conclusions, based
on the coefficients, are noted on the chalkboard. Also, they are asked how successful a consumer
would be in obtaining quality by picking the highest- or lowest-priced brands. With regard to
canned red kidney beans, there is a strong association between quality and price. Unfortunately
for consumers, the relationship is in the wrong direction as expressed by the –.90 coefficient.