Are prices really higher in department stores as compared to off-price stores? Kirby and Dardis examined prices of 20 items (shirts, pants, etc.) for 13 weeks and found that prices are indeed 40% higher in department stores.13 The ANOVA table, adapted from their report, is shown in Table 15.5.6.
a. Are the higher prices (40% higher at department stores on average) significantly higher? How do you know?
b. What kind of ANOVA is this?
c. Identify the three factors in this analysis. How many categories are there for each one?
d. What does the p-value for main effect B tell you?
e. Are there significant differences in pricing from one week to another? How do you know?
f. Consider the interaction between type of store and item. Is it significant? What does this tell you?
g. Consider the interaction between type of store and week. Is it significant? What does this tell you?
h. Consider the interaction between item and week. Is it significant? What does this tell you?
i. Usually, we examine p-values only to see if they are small enough to declare significance. However, the three-way interaction p-value appears suspiciously large, suggesting that there may be significantly less randomness than was expected for this model. Which technical assumption of hypothesis testing may not be satisfied here?

TABLE 15.5.6 Analysis of Variance for Prices by Store Type, Item, and Week Degrees of Source of Variation Store type (A) tem (B) Week (C) Two-way interaction Sum of Squares 1,794,577,789 25,726,794,801 246,397,563 Mean Square 1,794,577,789 1,354,041 2,053,313 F Value 1, 121.52 864.21 12.83 p-Value 0.000000 0.000000 0.000000 19 12 970,172,936 69,197,628 320,970,292 19 12 228 510,617 5,766,469 140,776 31.91 3.60 0.88 0.000000 0.000027 0.884253 A x C B x C Three-way interaction 264,279,428 1,664,128,185 31,056,518,626 228 1040 1559 115,912 0.72 0.998823 Residual 1,600,123 Total