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Chapter 13: Q3BSC (page 597)

Sign Test vs. Wilcoxon Signed-Ranks Test Using the data in Exercise 1, we can test for no difference between body temperatures at 8 AM and 12 AM by using the sign test or the Wilcoxon signed-ranks test. In what sense does the Wilcoxon signed-ranks test incorporate and use more information than the sign test?

Short Answer

Expert verified

The sign test uses only the signs of the differences, while the Wilcoxon signed-ranks test uses both the sign as well as the magnitude of differences.

Step by step solution

01

Given information

Samples are given showing the body temperature at 8 a.m. and 12 a.m.

02

Describe the sign test and Wilcoxon signed-ranks test

Both the Sign test and the Wilcoxon signed-ranks test are used to test the difference between temperatures.

In the Wilcoxon signed-rank test, ranks are used to assign the differences between the paired set of values. The Wilcoxon signed-ranks test uses both the sign as well as the magnitude of differences, whereas the sign test uses only the sign of the differences.

Thus, the Wilcoxon signed-rank test gives a more appropriate picture as it uses a decent amount of information.

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Most popular questions from this chapter

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U.S. News&World Report ranks

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Using the Mann-Whitney U Test The Mann-Whitney U test is equivalent to the Wilcoxon rank-sum test for independent samples in the sense that they both apply to the same situations and always lead to the same conclusions. In the Mann-Whitney U test we calculate

\(z = \frac{{U - \frac{{{n_1}{n_2}}}{2}}}{{\sqrt {\frac{{{n_1}{n_2}\left( {{n_1} + {n_2} + 1} \right)}}{{12}}} }}\)

Where

\(U = {n_1}{n_2} + \frac{{{n_1}\left( {{n_1} + 1} \right)}}{2} - R\)

and R is the sum of the ranks for Sample 1. Use the student course evaluation ratings in Table 13-5 on page 621 to find the z test statistic for the Mann-Whitney U test. Compare this value to the z test statistic found using the Wilcoxon rank-sum test.

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R RRR D R D R RR D R RR D D R D D R R D R R D R D

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