16.8 SPSS Lesson 14: Non-parametric Tests

Gordon E. Sarty

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 :

SPSS screenshot © International Business Machines Corporation.

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

Running the test produces :

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 :

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 :

The output for the paired Wilcoxon signed rank test is :

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 :

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 :

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:

Running the test gives:

There is enough information to compute the test statistic $H$ which is labeled as Chi-Square in the SPSS output. That is $H = 40.218$ and it is significant ( $p = 0.000$ ) so at least one of the group means is significantly different from the others. Also we see $\nu = k-1 = 2$ . Notice that the sums of the ranks are not given directly but sum of ranks = Mean Rank $\times$ N.