In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.The five differences are to be assigned an appropriate rank.What rank should the difference of -7 be assigned?

A) 1
B) 2
C) 3
D) 4

Question

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below.

The data are to be analyzed using the Wilcoxon signed rank test.The five differences are to be assigned an appropriate rank.What rank should the difference of -7 be assigned?

A) 1
B) 2
C) 3
D) 4

Tracey Pamphile · Accepted Answer

Final Answer : B, Explanation :  To assign ranks, the absolute values of the differences are first calculated and then sorted in ascending order. The smallest absolute difference is assigned a rank of 1, the next smallest a rank of 2, and so on. If there are ties, the ranks are averaged. In this case, the absolute value of the difference of -7 is 7, which is the largest absolute difference. Therefore, it is assigned a rank of 1. The remaining absolute differences are 1, 3, 4, and 4 (ties between subjects 1 and 4 as well as subjects 2 and 3). These differences are ranked in ascending order as 2, 3.5, 3.5, and 5, respectively. Therefore, the difference of -7 should be assigned a rank of 1, which corresponds to choice B.

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