When to Use ANOVA — and When to Use Something Else

May 2026·6 min read

When to use ANOVA is straightforward once you know the rule: three or more groups, one metric dependent variable, and you want to compare means. ANOVA avoids the inflated error rate that comes from running multiple t-tests. This guide explains the difference between one-way, two-way, and repeated measures ANOVA, how to check its two key assumptions, and how to report η² in APA format.

What Is ANOVA? Comparing 3+ Groups Explained

ANOVA (Analysis of Variance) tests whether the means of three or more groups are significantly different from each other. Despite the name, it works by comparing variances — specifically, the variance between groups relative to the variance within groups (the F-ratio).

Typical thesis example: comparing stress levels across three study formats (in-person, hybrid, online). You have one independent variable (study format) with three levels, and one metric dependent variable (stress score). That is one-way ANOVA.

ANOVA tells you that at least one group differs — but not which ones. You need a post-hoc test for that.

One-Way vs. Two-Way vs. Repeated Measures ANOVA

Choose the ANOVA type based on your design:

• One-way ANOVA: one independent variable with 3+ levels, different participants in each group.
• Example: stress compared across three degree programmes.
• Two-way ANOVA (factorial ANOVA): two independent variables simultaneously.
• Example: stress compared by study format AND gender. Allows you to detect interaction effects.
• Repeated measures ANOVA: the same participants measured at three or more time points.
• Example: stress measured at start, mid-semester, and end of semester.

When to Use ANOVA vs. t-Test: The 3-Group Rule

The t-test handles exactly two groups. ANOVA handles three or more. The reason you cannot simply run multiple t-tests is statistical: each t-test carries a 5% Type I error risk. With three comparisons (A vs. B, A vs. C, B vs. C), the combined error rate rises to roughly 14%. ANOVA controls this by testing all groups simultaneously.

If normality fails: with n < 30 per group and Shapiro-Wilk p < .05, switch to Kruskal-Wallis (non-parametric ANOVA alternative).

If you have only two groups: use the t-test — a one-way ANOVA with two groups produces identical results.

Checking Assumptions: Normality and Levene’s Test in SPSS

ANOVA has two key assumptions:

1. Normality per group: Analyze → Descriptive Statistics → Explore → Dependent variable into Dependent List, grouping variable into Factor List → Plots → Normality plots with tests → OK. Check Shapiro-Wilk for each group (p > .05 = normality not violated).

2. Homogeneity of variance: run ANOVA via Analyze → Compare Means → One-Way ANOVA → Options → tick Homogeneity of variance test → OK. Levene’s p > .05 = variances are equal → use standard ANOVA. Levene’s p < .05 → use Welch’s F.

[TIP] With n > 30 per group, ANOVA is robust to mild normality violations due to the Central Limit Theorem. Check the Q-Q plot visually and proceed if deviations are minor.

Post-Hoc Tests: Tukey HSD Explained Simply

ANOVA’s F-test tells you that at least one group differs. A post-hoc test tells you which pairs differ.

Tukey HSD (Honest Significant Difference): use when Levene’s test is non-significant (equal variances). It controls the family-wise error rate across all comparisons.

Games-Howell: use when Levene’s test is significant (unequal variances). More conservative but reliable.

SPSS path: Analyze → Compare Means → One-Way ANOVA → Post Hoc → tick Tukey (or Games-Howell) → OK.

In the output, look at the Multiple Comparisons table: each pair shows a mean difference, standard error, and p-value. Pairs with p < .05 are significantly different.

Reporting η² as Effect Size in APA Format

• Significant ANOVA:
• "A one-way ANOVA revealed a significant effect of study format on stress scores, F(2, 118) = 7.43, p = .001, η² = .11." (η² = .11 is a medium effect; benchmarks: .01 small, .06 medium, .14 large.)
• With post-hoc:
• "Tukey HSD post-hoc comparisons indicated that students in the in-person format (M = 21.3, SD = 4.9) reported significantly lower stress than online students (M = 25.7, SD = 5.4, p = .002), but did not differ from hybrid students (M = 23.1, SD = 5.1, p = .082)."
• Non-significant:
• "No significant difference in stress was found across study formats, F(2, 118) = 1.24, p = .293, η² = .02."

[INFO] SPSS calculates eta-squared as part of the ANOVA output when you tick ‘Effect size’ in the Options dialog. Partial eta-squared and eta-squared are identical for one-way ANOVA.