To run a one-way ANOVA in SPSS you open Analyze > Compare Means and Proportions > One-Way ANOVA, put your continuous outcome in Dependent List and your group in Factor, tick Descriptive and the homogeneity of variance test under Options, and pick Tukey under Post Hoc. For a factorial design you use Analyze > General Linear Model > Univariate instead. This page shows the exact clicks, which number in the output decides the result, and how to write it in APA.
ANOVA, the analysis of variance, tests whether the mean of a continuous outcome differs across the levels of one or more categorical factors. A one-way ANOVA answers a single question: do three or more unrelated groups differ on average? A factorial ANOVA adds a second factor and asks two more questions on top of that, one main effect per factor plus the interaction between them. This guide is part of our statistics homework help and sits under our wider SPSS homework help. It gives the exact menu path, points at the one value in each table that decides the result, and shows how to report it.
One version note that trips people up. In SPSS version 29 and later the old Compare Means menu is named Compare Means and Proportions, so One-Way ANOVA now lives under Analyze > Compare Means and Proportions > One-Way ANOVA. Factorial and repeated-measures designs stay under Analyze > General Linear Model in every recent version.
Match your design to the right procedure, then follow its steps below.
| Your design | Your data | Procedure |
|---|---|---|
| One factor, three or more unrelated groups | Continuous outcome, one grouping variable | One-way ANOVA |
| Two factors, unrelated groups, and their interaction | Continuous outcome, two grouping variables | Factorial (two-way) ANOVA |
| One factor but group variances are unequal | Levene's test is significant | Welch's ANOVA with Games-Howell |
| The same people measured three or more times | Repeated measures, one group | Repeated-measures ANOVA |
Not sure your data meets the requirements? Both guides below list the assumptions and the fallback to use when one fails.
Compares the means of one continuous outcome across three or more unrelated groups, for example an exam score across three revision methods.
Assumptions. A continuous outcome, three or more independent groups, no serious outliers, approximate normality within each group (Shapiro-Wilk in Analyze > Descriptive Statistics > Explore), and equal variances, which SPSS checks with Levene's test from the Options checkbox. If normality is badly broken, switch to the Kruskal-Wallis H test.
Step one, read Levene's test. The Test of Homogeneity of Variances table decides which post-hoc test is valid. Read the Based on Mean row. If its Sig. is above .05 the variances are equal, so the standard ANOVA and Tukey are fine. If its Sig. is .05 or below the variances are unequal, so you read the Welch row of the output and use Games-Howell instead of Tukey.
| Levene Statistic | df1 | df2 | Sig. | |
|---|---|---|---|---|
| Based on Mean | 0.412 | 2 | 27 | .666 |
| Based on Median | 0.388 | 2 | 27 | .682 |
Here Sig. = .666, above .05, so the variances are equal and Tukey is the correct post-hoc test.
Step two, read the ANOVA table. The ANOVA table holds the omnibus result. Read the Between Groups row for the F ratio, its two degrees of freedom (Between Groups df, then Within Groups df) and the Sig. A Sig. below .05 means at least one group mean differs from the others, though it does not yet say which.
| Sum of Squares | df | Mean Square | F | Sig. | |
|---|---|---|---|---|---|
| Between Groups | 85.5 | 2 | 42.7 | 4.467 | .021 |
| Within Groups | 258.3 | 27 | 9.6 | ||
| Total | 343.8 | 29 |
Step three, read the Tukey comparisons. Because the omnibus test is significant, the Multiple Comparisons table shows every pair of groups. An asterisk on the Mean Difference flags a pair that differs significantly, and the Sig. column gives the exact p-value for that pair. Each pair appears twice with the sign reversed, so read one direction and ignore the mirror.
| (I) Method | (J) Method | Mean Difference (I−J) | Std. Error | Sig. |
|---|---|---|---|---|
| Method A | Method B | −3.30* | 1.39 | .046 |
| Method A | Method C | −3.80* | 1.39 | .034 |
| Method B | Method C | −0.50 | 1.39 | .989 |
The asterisks show Method A differs from both Method B and Method C, while Method B and Method C do not differ from each other.
Common mistakes
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Tests two categorical factors at once, for example revision method and gender, and the interaction between them, on one continuous outcome.
Assumptions. A continuous outcome, two independent categorical factors, no serious outliers, approximate normality of the residuals, and equal variances across all factor combinations, which Levene's test checks from the Options checkbox.
What to read. The Tests of Between-Subjects Effects table. Read the row for each factor and the interaction row, taking F, Sig. and Partial Eta Squared from each. Read the interaction first: a significant interaction means the effect of one factor depends on the level of the other, and the main effects are then interpreted with care. Ignore the Corrected Model, Intercept and Error rows for reporting.
| Source | Type III SS | df | Mean Square | F | Sig. | Partial η² |
|---|---|---|---|---|---|---|
| Method | 78.4 | 1 | 78.4 | 8.94 | .005 | .199 |
| Gender | 9.8 | 1 | 9.8 | 1.12 | .297 | .030 |
| Method * Gender | 45.7 | 1 | 45.7 | 5.21 | .028 | .126 |
| Error | 315.6 | 36 | 8.77 |
Common mistakes
A significant F tells you an effect exists; partial eta squared tells you how big it is.
What it is. Partial eta squared is the proportion of variance in the outcome explained by a factor, after the variance explained by the other factors is set aside. It runs from 0 to 1. The common benchmarks from Cohen are 0.01 for a small effect, 0.06 for a medium effect and 0.14 for a large effect.
Where to find it. In a factorial design, tick Estimates of effect size under Options in General Linear Model, and SPSS adds the Partial Eta Squared column to the Tests of Between-Subjects Effects table shown above. For a one-way design run through Compare Means and Proportions, the ANOVA table does not print it, so either read the ANOVA Effect Sizes table that SPSS version 27 and later adds below the ANOVA table, or run the same model through General Linear Model, Univariate to get partial eta squared directly. For a single-factor model, partial eta squared equals eta squared, which is the Between Groups sum of squares divided by the Total sum of squares.
Most ANOVA marks are lost not on the software but on ignoring a broken assumption. Check the assumption, and when it fails, switch to the matched approach rather than reporting an invalid result.
| Assumption | How SPSS checks it | If it fails |
|---|---|---|
| Normality within groups | Shapiro-Wilk and Q-Q plots in Explore | Use the Kruskal-Wallis H test |
| Equal variances | Levene's test (Homogeneity of variance) | Read the Welch row and use Games-Howell |
| No serious outliers | Boxplots in Explore | Investigate, and report with and without the point |
| Independence of observations | Study design, not a test | Use a repeated-measures or mixed model |
Procedures on this page were checked against the IBM SPSS Statistics documentation, the UCLA statistical computing SPSS guides and the Kent State University SPSS tutorials.
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The F value is the ratio of the variance between the group means to the variance within the groups. A larger F means the group means are spread further apart than you would expect from chance alone. On its own it means little; you read it together with its two degrees of freedom and the Sig. column, and a Sig. below your alpha, usually 0.05, tells you at least one group mean differs.
When Levene's test is not significant and the group sizes are similar, Tukey's HSD is the standard choice for comparing every pair of means. When Levene's test is significant, the equal-variances assumption is broken, so you switch to Welch's ANOVA and use the Games-Howell post-hoc, which does not assume equal variances. Only run post-hoc tests when the overall ANOVA is significant.
Partial eta squared is an effect size that reports the proportion of variance in the outcome explained by a factor, after the variance explained by the other factors is removed. It runs from 0 to 1, with rough benchmarks of 0.01 small, 0.06 medium and 0.14 large. SPSS prints it in the General Linear Model output when you tick Estimates of effect size under Options.
A one-way ANOVA has one factor and tests whether the outcome differs across its groups. A factorial, or two-way, ANOVA has two or more factors and tests each main effect plus the interaction between them, which asks whether the effect of one factor depends on the level of the other. One-way ANOVA lives under Compare Means and Proportions; factorial ANOVA lives under General Linear Model, Univariate.
Use Welch's ANOVA when Levene's test of homogeneity of variances is significant, meaning the group variances are not equal. In the One-Way ANOVA dialog, click Options and tick Welch to get the resistant test, then pair it with the Games-Howell post-hoc instead of Tukey.
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