# Analysis of Variance with SPSS – Problem 10.2: Post Hoc Multiple Comparison Tests

Now we will introduce the concept of post hoc multiple comparisons, sometimes called follow­up tests. When you compare three or more group means, you know that there will be a statistically significant difference somewhere if the ANOVA F (sometimes called the overall F or omnibus F) is significant.

However, we would usually like to know which specific means are different from which other ones. In order to know this, you can use one of several post hoc tests that are built into the one­way ANOVA program. The LSD post hoc test is quite liberal and the Scheffe test is quite conservative so many statisticians recommend a more middle of the road test, such as the Tukey HSD (honestly significant differences) test, if the Levene’s test was not significant, or the Games-Howell test, if the Levene’s test was significant. Ordinarily, you do post hoc tests only if the overall F is significant. For this reason, we have separated Problems 10.1 and 10.2, which could have been done in one step. Fig. 10.3 shows the steps one should use in deciding whether to use post hoc multiple comparison tests.

Fig. 10.3. Schematic representation of when to use post hoc multiple comparisons with a one-way ANOVA.

• If the overall F is significant, which pairs of means are significantly different?

After you have examined Output 10.1 to see if the overall F (ANOVA) for each variable was significant, you will do appropriate post hoc multiple comparisons for the statistically significant variables. We will use the Tukey HSD if variances can be assumed to be equal (i.e., the Levene’s test is not significant) and the Games-Howell if the assumption of equal variances cannot be justified (i.e., the Levene’s test is significant).

First we will do the Tukey HSD for grades in h.s. Open the One-Way ANOVA dialog box again by doing the following:

• Select Analyze  Compare Means  One-Way ANOVA… to see Fig. 10.1 again.
• Move visualization test out of the Dependent List: by highlighting it and clicking on the arrow pointing left because the overall F for visualization test was not significant. (See interpretation of Output 10.1.)
• Also move math achievement to the left (out of the Dependent List: box) because the Levene’s test for it was (We will use it later.)
• Keep grades in the Dependent List: because it had a significant ANOVA, and the Levene’s test was not significant.
• Insure that father’s educ revised is in the Factor
• Your window should look like Fig. 10.4.

• Next, click on .. and remove the check for Descriptive and Homogeneity of variance test (in Fig. 10.2) because we do not need to do them again; they would be the same.
• Click on Continue.
• Then, in the main dialogue box (Fig. 10.1), click on Post Hoc. to get Fig. 10.5.
• Check Tukey because, for grades in h.s., the Levene’s test was not significant so we assume that the variances are approximately equal.

• Click on Continue and then OK to run this post hoc test.

Compare your output to Output 10.2a

Output 10.2a: Tukey HSD Post Hoc Tests

/MISSING ANALYSIS

/POSTHOC = TUKEY ALPHA(0.05).

After you do the Tukey test, let’s go back and do Games-Howell. Follow these steps:

• Select Analyze  Compare Means  One-Way ANOVA…
• Move grades in h.s. out of the Dependent List: by highlighting it and clicking on the arrow pointing left.
• Move math achievement into the Dependent List:
• Insure that father’s educ revised is still in the Factor:
• In the main dialogue box (Fig. 10.1), click on Post Hoc. to get Fig. 10.4.
• Check Games-Howell because equal variances cannot be assumed for math achievement.
• Remove the check mark from Tukey.
• Click on Continue and then OK to run this post hoc test.
• Compare your syntax and output to Output 10.2b.

Output 10.2b: Games-Howell Post Hoc Test

ONEWAY mathach BY faedRevis

/MISSING ANALYSIS

/POSTHOC = GH ALPHA(0.05).

Oneway

Interpretation of Output 10.2