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6 15 = 1 (14.28) (12-1) where the d, are the differences of the ranked pairs. The following tests of the null hypothesis H of no association in the popu- lation have a significance level a. 1. To test against the alternative of positive association, the decision rule is as follows: reject H, if r> (14.29) 2. To test against the alternative of negative association, the decision rule is as follows: reject Hair, 150/2 V16 (14.31) Example 14.15 Cruise Industry Promotion (Spearman Rank Correlation) To promote the cruise industry in Florida, suppose that James Thorne of the Cruise Emporium of Ormond Beach ran an advertisement in 17 tourism magazines. Readers were invited to write for additional brochures and literature. The two variables to be related are X: cost of advertising and circulation, in thousands of dollars Y: return-on-inquiry cost where the latter is defined as Y = (estimated revenue from inquiries - cost of advertisement) = cost of advertisement Table 14.19 lists the ranks of these two variables for the 17 magazine advertise- ments. Calculate the Spearman rank correlation coefficient and test for association be- tween the variables. Table 14.19 Rank Correlation Calculations for the Cruise Example MAGAZINE RANK(X) RANK(Y) di = RANK(x) - RANK(Y) 1 14 2 12 144 2 8 4 4 16 3 1 16 -15 225 4 16 1 15 225 5 17 5 12 144 6 13 6 7 49 7 15 8 7 49 8 2 11 -9 81 9 7 9 -2 4 10 3 13 -10 100 11 6 12 -6 36 12 9 17 -8 64 13 5 3 2 4 14 4 7 -3 9 15 11 14 -3 9 16 12 15 -3 9 17 10 10 0 0 Sum 1,168