One-Way ANOVA in SPSS: Post-Hoc Tests and Effect Size

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When Do You Use One-Way ANOVA?

One-way ANOVA compares the means of three or more independent groups on a continuous outcome variable. Running multiple t-tests instead inflates the Type I error rate. Examples: Do three teaching methods produce different learning outcomes? Does anxiety level differ across four age groups?

ANOVA Assumptions

• Normality: The dependent variable should be approximately normal within each group.
• Homogeneity of variance: Levene's test should be non-significant (p>0.05).
• Independence of observations.

Running One-Way ANOVA in SPSS

Navigate to Analyze → Compare Means → One-Way ANOVA.

1. Move the outcome variable to Dependent List.
2. Move the grouping variable to Factor.
3. Click Post Hoc: select Tukey (equal sample sizes, homogeneous variances) or Games-Howell (unequal sizes or variances).
4. Click Options: check Descriptive, Homogeneity of variance test, and Means plot.

Interpreting the Output

In the ANOVA table, look at the F statistic and Sig. value. p<0.05 means at least one pair of groups differs significantly. The Post Hoc Tests table reveals which specific pairs differ — an asterisk (*) marks significant pairs.

Effect Size: Eta Squared (η²)

Statistical significance alone is insufficient. Report effect size to convey practical importance. Enable Estimates of effect size in Options to get Partial Eta Squared (η²p). Guidelines: .01=small, .06=medium, .14=large effect.

APA Reporting Example

A one-way ANOVA revealed a statistically significant effect of education level on income, F(2, 147)=18.63, p<.001, η²=.20. Tukey post-hoc tests indicated that university graduates (M=$52,400, SD=$11,200) earned significantly more than both high school graduates (M=$38,600, SD=$8,300, p=.001) and primary school graduates (M=$26,100, SD=$6,100, p<.001).

When Assumptions Are Violated

If normality or variance homogeneity is not met, use the Kruskal-Wallis test — the non-parametric equivalent of one-way ANOVA.

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