Question 14.65

14.65 Considering a transformation.

CASE 14.1 In Example 14.8 (pages 723–724), we compared the likelihood to purchase among three groups. We performed ANOVA, even though the data were non-Normal with possible nonconstant variance, because of the robustness of the procedure. For this exercise, let’s consider a transformation.

moral

  1. We have data that must be between 0 and 100. This kind of constraint can result in skewed distributions and unequal variances in a similar fashion to the binomial distribution as moves away from 0.5 toward 0 or 1. For data like these, there is a special transformation, the arcsine square root transformation, that often is helpful. Construct this new response variable

  2. Construct histograms of this response variable for each population. Compare the distributions of the transformed variable with those in Figure 14.3 (page 716). Does the spread appear more similar? Do the data also look more Normal?
  3. Perform ANOVA on the transformed variable. Do the results vary much from those in Figure 14.8?

14.65

(b) The distributions of the transformed data are much more Normal than the original likelihood histograms. The spreads are all very similar now between 0.2 and 0.25. (c) . There are significant differences among groups for the transformed data. The results of this ANOVA are quite similar to the results of the ANOVA on the untransformed data.