ANOVA is an extension of the two group difference of means test (t-test). The t-test is used to compare two group means, but ANOVA allows for comparing three or more group means, which is easier than conducting numerous t-tests.

To conduct a One-Way Analysis of Variance (ANOVA) test in SPSS, you must first begin by choosing two variables. The variables we will use in this example are religious affiliation and frequency of prayer. Basically we are asking, “Does religion affiliation have an influence on how often people pray?”

Once you know what you want to compare, you can tell SPSS to run the analysis by clicking on “Analyze” → “Compare Means” → “One-Way ANOVA”:

The One-Way ANOVA dialog box will appear:

In the list displayed on the left, click on the variable that corresponds to your dependent variable (should be an interval/ratio variable). In our example this is frequency of prayer. Move it into the Dependent List by clicking on the upper arrow button. In this example, we are asking if religious preference has any effect on how often people pray.

Now select the (quasi) independent variable from the list on the left and click on it. Move it into the Factor box by clicking on the lower arrow button. In our example this is religious affiliation.

Click on the Options button in the One-Way ANOVA dialog box. The One-Way ANOVA dialog box appears:

Click in the check box to the left of Descriptives (to get descriptive statistics), Homogeneity of Variance (to get a test of the assumption of homogeneity of variance) and Means plot (to get a graph of the means of the conditions).

Click on the Continue button to return to the One-Way ANOVA dialog box. In the One Way ANOVA dialog box, click on the “OK” button to perform the analysis of variance. The SPSS output window will appear. The output consists of six major sections. The first is the descriptives section:

The Descriptives table provides various descriptives for the groups being compared, including the group sample size, mean, standard deviation, minimum, maximum, standard error, and confidence interval for the mean. In this example, there were 64 Jewish individuals, the mean frequency of prayer was 4.70 (on a six point scale; technically it is an interval-like ordinal variable), and the standard deviation was 1.217. There were 132 Catholic individuals with a mean frequency of prayer at 3.38, and a standard deviation of 1.438.

The ANOVA output gives us the analysis of variance summary table. There are six columns in the output:

Column Description
Unlabeled (source of variance) This column describes each row of the ANOVA summary table. It tells us that the first row corresponds to the between-groups estimate of variance. The between-groups estimate of variance forms the numerator of the F ratio. The second row corresponds to the within-groups estimate of variance. The within-groups estimate of variance forms the denominator of the F ratio. The final row describes the total variability in the data.
Sum of Squares The sum of squares column gives the sum of squares for each of the estimates of variance.
Df The third column gives the degrees of freedom for each estimate of variance. The degrees of freedom for the between-groups estimate of variance are given by the number of levels of the IV-1. In this example there are five levels of the independent variable.
Mean Square The fourth column gives the estimates of variance (the mean squares). Each mean square is calculated by dividing the sum of square by its degrees of freedom.
F The fifth column gives the F ratio. It is calculated by dividing mean square variance between-groups by the mean square variance within groups.
Sig. The final column gives the significance of the F-ratio. This is the p-value. If the p-value is less than or equal to your alpha level, then you can reject null hypothesis that all means are equal. In our example, the p-value is .000.

Here is the actual ANOVA table from the example:

Based on this analysis, we can conclude that religious affiliation does significantly affect frequency of prayer for genetic counselors.

Chapter contributed by Sheena Wright.