One-way ANOVA

Analysis of variance (ANOVA) is used when comparing the mean scores of more than two groups. One-way analysis of variance involves one independent variable (referred to as factor) which has a number of different levels (groups or conditions). The dependent variable is a continuous variable.

Analysis of variance compares the variability in scores between the different groups and the variability within each group. An F ratio is calculated; a large F ratio indicates that there is more variability between the groups (cause by the independent variable) than there is within each group (error term). A significant F test indicates that the groups differ. However, it does not indicate which of the groups differ. For this, you will need to conduct post-hoc tests.

1. Click on Analyze\Compare Means\One-way ANOVA.
2. Move your dependent continuous variable into the Dependent List box.
3. Move your independent categorical variable into the box Factor.
4. Click the Options button and click on Descriptive, Homogeneity of variance test, Brown-Forsythe, Welch and Means Plot.
5. For Missing Values, make sure that you mark Exclude cases analysis by analysis.
6. Click on the button Post Hoc and click on Tukey.
7. Click on Continue and OK.

Homogeneity of variances

Levene’s test of homogeneity of variances tests whether the variance in scores is the same for each of the three groups. If the Sig. value is greater than .05, you have not violated the assumption of homogeneity of variance. If you have violated this assumption, check the Robust Tests of Equality of Means and use Welch and Brown-Forsythe tests.

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Significance of the test

To assess whether there is a statistically significant difference between the groups, refer to the Sig value in the ANOVA table.

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Post-hoc tests

If you have found a significant difference in the overall ANOVA, look at the Multiple Comparisons table to assess what groups are significantly different from one another.

Reprint Courtesy of International Business Machines Corporation, © International Business Machines Corporation. SPSS Inc. was acquired by IBM in October, 2009.

In the example above, the High School and University groups differ significantly in Total Mastery.

Effect size

The effect size, or magnitude of the differences between groups, can be calculated using information provided in the ANOVA table:

Eta square= Sum of squares between groups/ Total sum of squares