A Gentle Introduction to Statistics Using SAS Studio (Hardcover edition) by Ron Cody

Author:Ron Cody [Ron Cody]
Language: eng
Format: epub, pdf
Publisher: SAS Institute
Published: 2019-09-26T16:00:00+00:00

Next, click the OPTIONS tab. For this example, you are using all the default values except for a request for Pairwise multiple comparison analysis (asymptotic only).

Figure 9.19: Options for the Analysis

Now that you have entered your choices on the DATA and OPTIONS tabs, it’s time to run the task. The first part of the output is shown in Figure 9.20.

Figure 9.20: Results from the Wilcoxon Rank Sum Test

To perform the Wilcoxon Rank Sum Test, all the scores are sorted in order from the lowest score to the highest score. You then assign a rank to each score: the lowest score is rank 1, the next highest score is rank 2, and so on. If several scores are equal, the Wilcoxon test assigns the mean rank to each of the values (don’t worry about this detail for now). Along with the fish weights, you also know the species associated with each rank. There is a total of 71 fish weights (34 + 20 + 17), so the ranks range from 1 to 71. If the null hypothesis is that the fish are all about the same weight, you would expect the sum of ranks for each species to be about the same. You use this idea to form your null hypothesis. If one or more of the fish species has a very high or low sum of ranks, you might expect that there are differences in weight based on species.

The table above shows the sum of ranks for each of the fish species and the expected value if the null hypothesis is true. Notice that the sum of Scores for Roach (224.5) is much lower than the sums for Bream or Pike, making you suspect that Roach are typically lighter than either Bream or Pike. To decide whether you should reject the null hypothesis that all the three species have equal weights, you look at the p-value at the bottom of Figure 9.20. Because the p-value is shown as <.0001, you reject the null hypothesis and conclude that one or more pairs of means are significantly different. But, which pairs of fish species are different? We will answer that question in a minute.

The next part of the output shows box plots for each fish species. Box plots are appropriate for this display because you are conducting a nonparametric test.

Figure 9.21: Box plots for Each Species

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