16. Non-parametric Tests

16.8 SPSS Lesson 14: Non-parametric Tests

16.8.1 Mann Whitney/Wilcoxson Rank Sum

The Mann Whitney/Wilcoxson Rank Sum tests is a non-parametric alternative to the independent sample t-test. So the data file will be organized the same way in SPSS: one independent variable with two qualitative levels and one independent variable. Open “RetinalAnatomyData.sav” from the textbook Data Sets :

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Choose Analyze \rightarrow Nonparametric Tests \rightarrow Legacy Dialogues \rightarrow 2 Independent Samples. Then set-up :

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Running the test produces :

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The first table has sums of the ranks including the sum of ranks of the smaller sample, R, and the sample sizes n_{1} and n_{2} that you could use to manually compute z_{\rm test} if you wanted to. The test statistic z_{\rm test} shows up in the second table along with p = 0.001 which means that you can marginally reject H_{0} for a two-tail test. When we did this test by hand, we required n_{1}, n_{2} \geq 10 so that the z test statistic would be valid. In the SPSS output two other test statistics, U and W that can be used for smaller sample sizes. The exact p-value is given in the last line of the output; the asymptotic p-value is the one associated with z_{\rm test}. When the asymptotic p-value equals the exact one, then the z test statistic is a good approximation — this should happen when n_{1}, n_{2} \geq 10.

16.8.2 Paired Wilcoxon Signed Rank Test and Paired Sign Test

Open “MigraineTriggeringData.sav” from the textbook Data Sets :

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We will see if there is a significant difference between pay and security (H_{0}: \mu_{d} = 0). Pull up Analyze \rightarrow Nonparametric Tests \rightarrow Legacy Dialogues \rightarrow 2 Related Samples to get :

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The output for the paired Wilcoxon signed rank test is :

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From the output we see that w_{s} = 10.50. The test statistic z_{\rm test} = -3.134 with p = 0.002 so the mean difference is significantly different from zero.

The output for the paired sign test (H_{0}: MD difference = 0) is :

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Here we see (remembering the definitions) that X_{\rm test} = 3. Since P = 0.013 we can conclude that “Skipping Meal” is significantly different from “Stress at Work” (more negative differences and the difference is significant).

16.8.3 Kruskal-Wallis Test

Open “CancerTumourReduction.sav” from the textbook Data Sets :

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The independent variable, group, has three levels; the dependent variable is diff. Choose Analyze \rightarrow Nonparametric Tests \rightarrow Legacy Dialogues \rightarrow K Independent Samples and set up the dialogue menu this way, with 1 and 3 being the minimum and maximum values defined in the Define Range menu :

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Running the test gives :

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There is enough information to compute the test statistic H which is labeled as Chi-Square in the SPSS output. That is H = 51.000 and it is significant (p = 0.000) so at least one of the group means is significantly different from the others. Also we see \nu = k-1 = 1. Notice that the sums of the ranks are not given directly but sum of ranks = Mean Rank \times N.