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

One-way ANOVA compares the means of three or more independent groups in a single test. In SPSS, use Analyze > Compare Means > One-Way ANOVA, ask for Levene's test, Welch's test and post hoc comparisons, and report eta squared as the effect size. A significant F only tells you that at least two groups differ; post hoc tests tell you which ones.

When to use one-way ANOVA

• One continuous dependent variable (for example purchase intention).
• One categorical factor with three or more independent groups (for example age groups, education levels, countries).

With only two groups, use the independent samples t-test. With two factors at once (age and gender), use a two-way ANOVA through Analyze > General Linear Model > Univariate.

Assumptions

1. Independent observations.
2. Approximate normality of the dependent variable in each group (robust with 30+ per group).
3. Homogeneity of variances, tested with Levene's test.

Run one-way ANOVA in SPSS

1. Go to Analyze > Compare Means > One-Way ANOVA.
2. Move purchase intention (PI) to Dependent List and age group to Factor.
3. Tick Estimate effect size for overall tests (SPSS 27 and later).
4. Options: tick Descriptive, Homogeneity of variance test, Welch and Means plot.
5. Post Hoc: tick Tukey (equal variances) and Games-Howell (unequal variances).
6. Click OK.

Read the output

Descriptives

Test of Homogeneity of Variances

Read the row Based on Mean. Here Levene's statistic = 1.98, p = .14: variances are homogeneous, so the classic F test and Tukey are appropriate. If p ≤ .05, report Welch's F and Games-Howell instead.

ANOVA table

The difference between age groups is significant: F(2, 297) = 8.25, p < .001.

Effect size

SPSS shows eta squared in the ANOVA Effect Sizes table. Here η² = .05 (12.0 / 228.0). Benchmarks from Cohen (1988): .01 small, .06 medium, .14 large. Age explains about 5% of the variance in purchase intention, a small to medium effect. Omega squared, also given by SPSS, is a less biased alternative.

Post hoc tests (Tukey HSD)

Only the youngest and oldest groups differ significantly. The means plot shows a steady decline with age.

How to report the result

A one-way ANOVA showed a significant effect of age group on purchase intention, F(2, 297) = 8.25, p < .001, η² = .05. Levene's test confirmed homogeneity of variances (p = .14). Tukey post hoc comparisons indicated that respondents aged 18–24 (M = 3.85, SD = 0.80) reported higher purchase intention than those aged 35 and over (M = 3.35, SD = 0.92, p < .001). Other differences were not significant.

Which post hoc test to choose?

If the assumptions are not met

Use Welch's F when variances differ. For strongly skewed data with small groups, use the non-parametric Kruskal-Wallis test: Analyze > Nonparametric Tests > Legacy Dialogs > K Independent Samples.

FAQ

F is significant but no post hoc test is. Why?

The overall F can pick up a pattern spread across several groups that no single pairwise comparison captures. Report it honestly and look at the means plot.

Can I use ANOVA with a Likert item as the dependent variable?

Prefer a composite score of several items. A single ordinal item is better analysed with Kruskal-Wallis.

What about repeated measures?

If the same respondents are measured several times, use Analyze > General Linear Model > Repeated Measures.

References

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.
• Field, A. (2024). Discovering statistics using IBM SPSS Statistics (6th ed.). Sage.
• Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863