Testing the assumptions of an ANOVA Assumptions: 1 The data are independent 2 The dependent variable is continuous 3 The residuals are normally distributed (look at histogram, Shapiro-Wilk) (If not transform the variable, do a Kruskall-Wallis, or bootstrap) 4 The residuals must be homoscedastic (look at boxplot, Levene's test) (If not do a Welch's ANOVA or bootstrap)

Using SPSS to perform a one-way ANOVA Open the data set TestScores.sav. Click on Analyze, General Linear Model > Univariate (Figure 6.4) Place TestScore in the Dependent Variable box and NativeLang in Fixed Factor(s) box.

Figure 6.4. The one-way ANOVA dialog box.

Click on Post Hoc. The post hoc dialog box appears (Figure 6.5). In that box, move NativeLang to Post Hoc Tests for box. Check Tukey and Bonferroni > Continue. Click on the Save button and check Unstandardized in the Predicted Values box and Unstandardized in the Residuals box > Continue. Click on Options. In the Options box move NativeLang to Display Means for box. Check Compare main effects. From the Confidence interval adjustment drop-down menu choose Bonferroni. Check Descriptive statistics, Estimates of effect size, and Homogeneity tests, Continue > OK (Figure 6.6).

Figure 6.5. The post hoc dialog box.

Figure 6.6. The One-Way ANOVA Options box.

Using SPSS to generate graphs and measures of normal distribution Click on Analyze > Descriptive Statistics > Explore. Click on the variable name of the residuals, RES_1, and move it to the Dependent List by clicking on the arrow between the boxes. Click on Statistics > check the box next to Descriptives > Continue. Click on Plots, check the boxes next to Histogram and Normality plots with tests > Continue > OK. In order to superimpose the normal distribution curve on the histogram double click on the histogram itself then in the Chart Editor choose Elements > Show Distribution Curve.

Using SPSS to test homoscedasticity Graphs > Legacy Dialogs > Boxplot > Simple > Define. Put RES_1 in Variable box and Native Language in Category Axis box > OK. The results of the Levene's test also tells you if the variance significantly differ from each other: Levene's Test of Equality of Error Variances F

df1 4.978

df2 2

Sig. 27

.014

Using SPSS to perform a Welch's one-way ANOVA Click on Analyze > Compare Means > One-way ANOVA. Move TestScore to the Dependent List and NativeLang to Factor box. Click on Options button and check Welch > Continue. Click on Post Hoc, check Tamhane's T2 > Continue > OK. Be sure that your independent variable is coded as a number, not a string or SPSS won't let you put it in the Dependent List.

Using SPSS to perform a Kruskal-Wallis H test Let's assume that the test score analysis results in a non-normal distribution of the residuals and so we need to perform a Kruskal-Wallis H test on the data. Open the file TestScores.sav. Click on Analyze > Nonparametric Tests > Independent Samples. Click on Objective tab and make sure Automatically compare distributions across groups is checked (Figure 6.7). Choose the Fields tab. Move Test Score into the Test Fields box and NativeLang into the Groups box > Run (Figure 6.8).

Figure 6.7. Kruskall-Wallis Objective tab.

Figure 6.8. Kruskal-Wallis Field tab.

The results of the Kruskal-Wallis H test appear as in Figure 6.9. To see this double click on the Hypothesis Test Summary box (Figure 6.10). The results would be reported as: H (2) = 10.315, p < . 006, two-tailed. To see the post hoc test: At the bottom of the screen, below Figure 6.9, in the View drop-down box, choose Pairwise Comparisons (Figure 6.11). The post hoc results appear as in Figure 6.12.

Figure 6.9. Results of the Kruskal-Wallis H test on the test score data.

Figure 6.10. Hypothesis Test Summary box.

Figure 6.11. View drop-down box.

Figure 6.12. Kruskal-Wallis post hoc results.

Using SPSS to bootstrap an ANOVA The only difference between carrying out a regular one-way ANOVA and one with bootstrapping is that you have to add one step to the process. Once you get to the main dialog box (Figure 6.20) if bootstrapping is available there will be a Bootstrap button. Click on it to bring up the Bootstrap dialog box, and click on Perform boostrapping > Continue.