7 Comparison of differences between more than 2 groups: Oneway ANOVA and Kruskal-Wallis Test We will first stay on the left-hand side of the decision tree, covering tests for independent samples. Oneway ANOVA The name ANOVA is short for Analysis of Variance and as you can guess from the name (and see from the decision tree) the Homogeneity of Variance (e.g. the Levene test) is a crucial assumption for this test. Incidentally, in exercise 5.1 and 5.2, where we learned how to do the Levene test, we have already learned how to do the Oneway ANOVA. Experimental data (for exercises 7.1-7.4): We have collected serum from healthy and diseased male and female subjects (e.g. we have 4 groups) and we have measured the concentration of a protein (in pg/ml) in this serum in the laboratory. Exercise 7.1: 1. In the Excel spreadsheet “Excercises_3”, select the tab “ANOVA I”. 2. Copy and paste the raw data into the SPSS “Data View” tab. 3. Label the data appropriately in the “Variable View” tab (use the variable name Grouping with the 4 groups and define the groups in Values). 4. In the menu bar, go to Analyse-> Compare Means->One way ANOVA (see exercise 5.1). 5. Transfer the variables to the correct boxes. 6. Tick the box for the homogeneity of variance test. 7. Select O.K. 8. The SPSS Output Window shows that the Levene test is not significant, therefore our data follow homogeneity of variance and we can continue looking at the ANOVA table. The pvalue for the ANOVA can be found at the very end of the ANOVA table, underneath the heading Sig. (see screen shot). The p-value is highly significant (pNonparametric tests->Legacy dialogs->K Independent Samples (see screen shot). 2

5. As soon as you select “K Independent Samples”, a new small window called “Tests for Several Independent Samples” opens up, with several selection options. 6. Using the top blue arrow, transfer “Serum Protein” over into the box called “Test Variable List”. 7. Using the bottom blue arrow, transfer “Grouping” over into the box called “Grouping Variable” (see screen shot).

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8. Select the blue box “Define Range” underneath the “Grouping Variable”. This opens up a new small window called “Several Independent Samples: Define Range”. 9. Type 1 in the box “Minimum” and type 4 in the box “Maximum” (see screen shot). Note: if we had for example 8 groups, we would type 1 and 8.

10. Select “Continue” and “Ok”. 11. The SPSS Output Window contains 2 tables. The first table (Ranks) is an overview of which groups we have analysed and the second table (Test statistics) contains the p-value for our Kruskal-Wallis test at the bottom row (see screen shot). The p-value is 0.05), meaning that there is no difference in serum protein concentrations between any of the groups. We do not have to continue with “post-hoc” testing.

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