ANOVA (Analysis of Variance)

In a hurried conversation in the hall, your advisor told you to use ANOVA to analyze your dissertation data. She didn’t have time to answer any questions about what type of ANOVA to use.

Definition

You use ANOVA to find out whether the means (averages) of three or more groups of people differ. Names you might hear are one-way ANOVA and two-way ANOVA. Special types of ANOVA include MANOVA (Multivariate Analysis of Variance), ANCOVA (Analysis of Covariance), and MANCOVA (Multivariate Analysis of Covariance).

Example (One-Way ANOVA)

You want to compare how completely people fill out a survey, depending on how it is administered. One hundred fifty teachers all complete the same survey. The 150 teachers are divided into three groups: Fifty teachers fill it out online, fifty receive it via snail mail at home and mail it back, and fifty receive it in on paper in the teachers’ room at school and return it to the school office. Your hypothesis is that the teachers who fill out the survey online will skip the fewest questions.

Note. If the teachers are grouped by an additional factor, for example, gender (males and females), this becomes a two-way ANOVA having six groups of people.

Analysis

We run the ANOVA for you in SPSS.

Note. Sometimes it is more efficient to perform ANOVA in SPSS using a regression procedure.

Writeup

We write up the results formally in APA format, like this writeup for the above example.

The mean number of questions skipped online was 2.36 (N = 50; SD = 0.69), the mean number of questions skipped at home was 3.00 (N = 50; SD = 1.05), and the mean number of questions skipped in school was 3.34 (N = 50; SD = 1.00). A one-way ANOVA showed that there was at least one significant difference between groups (overall F = 14.36; p < .001). Post hoc tests using the Scheffe adjustment showed that significantly fewer questions were skipped by the teachers in the online group as compared to the at-home and in-school groups (N = 150; F = 24.97; p < .001). The effect size (f) was 0.40. Using Cohen’s (1988) conventions, this is a large effect.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. 2nd ed. Hillsdale, NJ: Lawrence Erlbaum

To see your dissertation results written up just like this, contact us!

Table

We also produce tables, like the following:

ANOVA of Number of Questions Skipped for the Three Survey Administration Methods

Source df Sum of squares Mean square F
Between-groups 2 24.76 12.38 14.36*
Within-groups 147 126.74 0.86
Total 149 151.50

*p < .001, two-tailed.

For theoretical help with your ANOVA analysis, running it in SPSS, or deciding whether ANOVA is the appropriate technique for your data, please contact us!