The following tablo ists body temperatures of seven subjects ar 8 AM and at 12 A

Question

The following tablo ists body temperatures of seven subjects ar 8 AM and at 12 AM. The data are matched pars because echparoftomeeratures is measured from the same person. Using the data, it possible to test for no dfference between body temperatures at 8 AM and 12 AM by using the sign test or the Wiloowon signed-ranks test. In what sense does the Wlcoxon signed-ranks test incorporate and use more information than the sign test? Temperature ("F) at 8AM_0 980 976 972 980 970 980 982 97.6 98.0 97.7 Temperature(F)at 12 AM 968 9 Choose the correct answer below. OA The sgn test uses only the signs of the aerences, butthew looon signed-ranks test uses ranks tat are affected by the magit des ofthe diferent O B. The sign test requires that the population is normally distributed, while the Wllooxon signed-ranks test only requires that the population distribution is approximately symmetric OC. The sgn test can only be used as a two-ailed test, while the wicoon signed-arks test an be used as a o·tailed or two-taled test. OD. The sig test uses ony the mag tudes of the dffere oes, but the wloonsgnedrarks test uses ranks that are flo ted by the mag tudes and the s gns of the dnerences

Explanation / Answer

The sign test is so called because it allocates a sign, either positive (+) or negative (-), to each observation according to whether it is greater or less than some hypothesized value, and considers whether this is substantially different from what we would expect by chance. If any observations are exactly equal to the hypothesized value they are ignored and dropped from the sample size.

The sign test is intuitive and extremely simple to perform. However, one immediately obvious disadvantage is that it simply allocates a sign to each observation, according to whether it lies above or below some hypothesized value, and does not take the magnitude of the observation into account. Omitting information on the magnitude of the observations is rather inefficient and may reduce the statistical power of the test. An alternative that does account for the magnitude of the observations is the Wilcoxon signed rank test.

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