One-Way ANOVA in SPSS: Procedure, Post Hoc Tests, and Output

A one-way ANOVA compares the means of three or more groups on a single continuous outcome using one categorical factor. SPSS runs it through two different procedures that land on the same F-test but produce different output: the dedicated One-Way ANOVA command and the more general GLM Univariate command. This guide covers both menu paths, how to check the homogeneity-of-variance assumption before you trust the result, the decision rule for choosing a post hoc test (Tukey HSD vs. Games-Howell), and how to read every table SPSS prints — Levene’s test, the ANOVA table, the post hoc comparisons, and the means plot — into a correctly reported result.

Two ways to run a one-way ANOVA in SPSS

Analyze > Compare Means > One-Way ANOVA (the submenu is labeled Compare Means and Proportions in SPSS Statistics 29 and later; One-Way ANOVA sits in the same place under either name) is the dedicated procedure for exactly this design: one continuous dependent variable, one categorical factor with three or more levels. It has built-in Post Hoc and Options buttons purpose-built for this comparison and is the simpler, more direct route for a genuinely one-factor design.

Analyze > General Linear Model > Univariate runs the identical omnibus F-test when you enter a single factor, but through the general linear model framework used for factorial and ANCOVA designs. Reach for GLM Univariate instead when you want partial eta-squared reported automatically (via its own Options > Estimates of effect size), when you expect to add a second factor or a covariate later and want the syntax to extend cleanly, or when you need estimated marginal means with covariate adjustment. For a genuinely single-factor comparison with no covariates, One-Way ANOVA is the more direct tool and is what the rest of this guide walks through.

Setting up the One-Way ANOVA dialog

Move your continuous outcome into the Dependent List box and your grouping variable into the Factor box — the factor must be coded as a categorical variable with three or more distinct integer values (two groups is a job for the independent-samples t-test instead). Three buttons matter for this guide:

• Post Hoc — opens the pairwise-comparison test menu, covered below.
• Options — check Descriptive (group N, mean, SD, SE, 95% CI), Homogeneity of variance test (this is what produces Levene’s test), and Means plot. SPSS Statistics 27 and later also add an Estimates of effect size checkbox here, which prints eta-squared and omega-squared for the omnibus F-test directly in the ANOVA table.
• Contrasts — only needed if you have specific, planned comparisons decided in advance of seeing the data; most applied work uses the omnibus test plus post hoc comparisons instead, which this guide covers.

Check homogeneity of variance before you pick a post hoc test

Run the procedure once with Homogeneity of variance test checked. SPSS prints a Test of Homogeneity of Variances table, typically with four rows — Based on Mean, Based on Median, Based on Median and with adjusted df, and Based on trimmed mean. The Based on Mean row is the traditional Levene’s test and the one most commonly reported; the other three are more robust variants used when the outcome is skewed.

• Levene’s Sig. > .05 — variances do not differ significantly across groups. The equal-variances assumption holds well enough to use a post hoc test that assumes it.
• Levene’s Sig. ≤ .05 — variances differ significantly across groups. Use a post hoc test built for unequal variances instead, regardless of how close the group sizes are.

This result is what decides which post hoc test to select next — run it first, not as an afterthought once you’ve already picked one.

Choosing a post hoc test: Tukey vs. Games-Howell

SPSS’s Post Hoc dialog splits pairwise comparison tests into two groups matching exactly the Levene’s result above:

• Equal Variances Assumed section: LSD, Bonferroni, Sidak, Scheffe, R-E-G-W F, R-E-G-W Q, S-N-K, Tukey, Tukey’s-b, Duncan, Hochberg’s GT2, Gabriel, Waller-Duncan.
• Equal Variances Not Assumed section: Tamhane’s T2, Dunnett’s T3, Games-Howell, Dunnett’s C.

The practical decision rule most applied researchers use:

• Levene’s test not significant → check Tukey HSD. It controls the family-wise Type I error rate across all pairwise comparisons while retaining reasonable power, and is the most widely reported equal-variances post hoc test in published work.
• Levene’s test significant → check Games-Howell. It does not assume equal variances or equal group sizes, uses a separate variance estimate and adjusted degrees of freedom for each pair (similar in spirit to a Welch-corrected comparison), and is generally preferred over Tamhane’s T2 in simulation studies for its balance of Type I error control and power under heterogeneous variances.

If you specifically need control over the family-wise error rate under a smaller, planned set of comparisons rather than all pairwise ones, see CASRAI’s guide to the Bonferroni correction for when that stricter, simpler alternative is the better fit than Tukey.

Reading the full SPSS output, table by table

A One-Way ANOVA run with Descriptive, Homogeneity of variance, Means plot, and a post hoc test all checked produces, in order:

• Descriptives — N, mean, SD, SE, and 95% CI for each group plus the total. Scan this first for wildly unequal group sizes, which is exactly when the Levene’s result below matters most.
• Test of Homogeneity of Variances — the Levene’s test rows described above. Read this before the ANOVA table, since it determines which post hoc table to trust.
• ANOVA — the omnibus test: a Between Groups row (Sum of Squares, df = k−1, Mean Square, F, Sig.), a Within Groups row (df = N−k), and Total (df = N−1). A significant Sig. here (≤ .05) tells you at least one pair of group means differs somewhere — it does not say which pair, which is exactly what the post hoc table answers next.
• Multiple Comparisons — the post hoc table, one row per pairwise group comparison, with Mean Difference (I−J), Std. Error, Sig., and a 95% confidence interval for the difference. SPSS marks significant pairs with an asterisk next to the mean difference as a shortcut, but always check the Sig. column itself.
• Homogeneous Subsets — produced only by range-style tests (Tukey HSD, Duncan, S-N-K, the R-E-G-W tests), not by Games-Howell or Tamhane’s T2. It groups the factor levels into subsets whose means don’t differ significantly from each other — a quick visual read of which groups cluster together, though the Multiple Comparisons table above remains the table you actually cite.
• Means Plot — a line chart of the factor levels against the dependent variable’s group means. Useful for presenting the pattern, but it carries no significance information on its own — the pairwise Sig. values still have to come from the Multiple Comparisons table.

Reporting the result

The standard APA-style write-up reports the omnibus test, then the specific pairwise differences the post hoc test flagged as significant:

“A one-way ANOVA showed a significant effect of condition on the outcome, F(2, 87) = 6.42, p = .003, η² = .13. Levene’s test was not significant, F(2, 87) = 1.18, p = .312, so Tukey HSD post hoc comparisons were used. Group A (M = 24.1, SD = 4.2) scored significantly higher than Group C (M = 20.3, SD = 3.9), p = .002, 95% CI [1.4, 6.2]; no other pairwise comparisons were significant.”

If Levene’s test had been significant instead, the write-up would state “Levene’s test was significant, F(2, 87) = 4.05, p = .021, so Games-Howell post hoc comparisons were used” in place of the Tukey sentence — the rest of the structure is identical.

Common mistakes to avoid

• Defaulting to Tukey without checking Levene’s test first. The whole point of the two post hoc sections in the dialog is that they answer the same question under different variance assumptions — picking Tukey out of habit when variances are unequal understates the real Type I error rate.
• Running separate independent-samples t-tests for every pair of groups instead of one ANOVA with post hoc tests. Multiple uncorrected t-tests inflate the family-wise error rate; the post hoc tests in the ANOVA procedure are built specifically to control it.
• Treating a significant omnibus F as proof every group differs from every other group. It only means at least one pair differs somewhere — the Multiple Comparisons table is what tells you which pair(s).
• Rounding an unequal-variances post hoc row’s adjusted values as if they came from a standard test. Games-Howell and Tamhane’s T2 use a separate error term per pair; report the numbers SPSS prints for that row exactly as given, the same way a Welch-corrected t-test’s non-integer df is reported as printed.

Frequently asked questions

What’s the difference between One-Way ANOVA and GLM Univariate in SPSS for a single factor?

Both produce the identical F, df, and Sig. values for a genuinely one-factor design — they run the same underlying model. One-Way ANOVA is the more direct route with its own Post Hoc and Options dialogs built for exactly this comparison; GLM Univariate is the better choice if you want partial eta-squared automatically, plan to add a second factor or covariate later, or need estimated marginal means.

How do I know whether to use Tukey or Games-Howell?

Check the Levene’s Test of Homogeneity of Variances result first. If it is not significant (Sig. > .05), use Tukey HSD. If it is significant (Sig. ≤ .05), use Games-Howell instead — it does not assume equal variances or equal group sizes.

What does a significant Levene’s test mean for my ANOVA?

It means the groups’ variances differ by more than chance would predict, so a post hoc test that assumes equal variances (like Tukey) is no longer the right choice for the pairwise comparisons — switch to an unequal-variances test such as Games-Howell. The omnibus ANOVA F-test itself is reasonably robust to moderate variance violations when group sizes are similar, but the post hoc choice should still follow the Levene’s result.

Do I need to run post hoc tests if the overall ANOVA is not significant?

No. A non-significant omnibus F (Sig. > .05) means the data don’t support concluding any group differs from any other, so there is nothing for the post hoc comparisons to follow up on — running and reporting them anyway invites exactly the uncorrected multiple-comparisons problem post hoc tests exist to prevent.

Can I get an effect size like eta-squared for a one-way ANOVA in SPSS?

Yes. SPSS Statistics 27 and later add an Estimates of effect size checkbox to the One-Way ANOVA Options dialog, which prints eta-squared and omega-squared alongside the ANOVA table. In GLM Univariate, the equivalent option reports partial eta-squared.

Why does the Homogeneous Subsets table not appear for my post hoc test?

It’s only produced by range-style tests — Tukey HSD, Duncan, S-N-K, and the R-E-G-W tests. Games-Howell and Tamhane’s T2 are pairwise-comparison-only tests and print a Multiple Comparisons table without a corresponding Homogeneous Subsets table; that isn’t an error.

Related CASRAI resources

For the underlying logic of the F-test, plus two-way and repeated-measures designs, see CASRAI’s ANOVA guide and the ANOVA dictionary term. If your outcome variable badly violates normality and a transformation isn’t appropriate, see the Kruskal-Wallis test, the nonparametric alternative to one-way ANOVA. For the two-group case, see CASRAI’s t-test in SPSS guide. For software background, see what SPSS is and who uses it, or compare it against alternatives in SPSS vs. R, SPSS vs. Stata, and jamovi vs. JASP (both free, SPSS-menu-style alternatives). For interpreting the effect-size figures this procedure can output, see the effect size term, and confirm your grouping variable is actually categorical rather than ordinal or continuous in CASRAI’s levels of measurement guide.