The promotional policies of four companies in a certain industry were compared to determine whether their rates for promoting blacks and whites differed. Data on the variable "rate discrepancy" were obtained for the four companies in each of three different two-year periods. This variable was defined as
d = W - B
where
W = (Number of whites promoted)(100) / Number of whites eligible for promotion
and
B = (Number of blacks promoted)(100) / Number of blacks eligible for promotion
The resulting data are reproduced in the following table.

a. Using dummy variables, create an appropriate regression model for this data set. Is this a randomized-blocks design?
b. Use the following table to test whether any significant differences exist among the average rate discrepancies for the four companies. Tukey's F for testing additivity equals 3.583 with 1 and 5 degrees of freedom.

c. Does Tukey's test for these data indicate that a removable interaction effect is present?
d. If no significant differences are found among the rate discrepancies for the four companies, would this support the contention that none of the companies has a discriminatory promotional policy?
e. Comment on the suitability of this analysis in view of the fact that the response variable is a difference in proportions.

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Company Period 12 Source d.F sS MS 42.2500 33800 1.600 845000 Periods Companies Error 2 6.0000 7.5000 2.0000 1.2500