How to Run an ANOVA in SPSS and Report It in APA (Step by Step)

A one-way ANOVA is the test you reach for the moment your research design compares three or more group means on a single continuous outcome — comparing test scores across three teaching methods, satisfaction ratings across four store locations, or reaction times across several experimental conditions. Running it correctly in SPSS and reporting it in APA 7 format is what separates a results section an examiner accepts from one that gets sent back with a red pen. This guide walks through every step, from checking assumptions to writing the final sentence.

What a one-way ANOVA actually tests

A one-way ANOVA tests whether the means of three or more independent groups differ significantly on one continuous dependent variable. “One-way” means there’s a single independent (grouping) variable — as soon as you have two independent variables, you’re into factorial ANOVA territory, which this guide doesn’t cover. The null hypothesis is that all group means are equal; a significant result tells you at least one group differs from at least one other, but not which ones — that’s what the post-hoc test in Step 5 is for.

Step 1: Check your assumptions

Before running the omnibus test, verify three assumptions:

• Independence of observations. Each participant appears in only one group — this is a design issue, not something SPSS checks for you.
• Normality within each group. Check via Analyze > Descriptive Statistics > Explore, selecting your dependent variable and grouping variable, and requesting Shapiro-Wilk statistics and Q-Q plots. With group sizes of roughly 15 or more per group, ANOVA is fairly robust to mild normality violations, but check anyway.
• Homogeneity of variance. Levene’s test, which SPSS can run automatically as part of the ANOVA procedure itself (see Step 2). A non-significant Levene’s result (p > .05) supports the assumption that variances are roughly equal across groups.

Step 2: Run the ANOVA in SPSS

1. Go to Analyze > Compare Means and Proportions > One-Way ANOVA (in older SPSS versions this menu is simply labelled Compare Means).
2. Move your continuous outcome variable into the Dependent List box.
3. Move your categorical grouping variable into the Factor box.
4. Click Post Hoc, tick Tukey, and click Continue.
5. Click Options, tick Descriptive and Homogeneity of variance test (this runs Levene’s test), and optionally tick Means plot for a visual comparison. Click Continue.
6. Click OK to run.

Step 3: Read the Descriptives and Levene’s test output

SPSS produces several tables. Start with two:

• Descriptives table: gives you the mean, standard deviation, and 95% confidence interval for each group. Record these — you’ll need the means and SDs for your results write-up and for any figures.
• Test of Homogeneity of Variance: this is Levene’s test. If the significance value is greater than .05, the assumption of equal variances holds and you can proceed with the standard ANOVA and Tukey post-hoc. If it’s significant (p < .05), the assumption is violated — see the section below on what to do instead.

Suppose you’re comparing exam scores (0–100) across three study-method groups (A = spaced practice, B = massed practice, C = no structured method), with 10 participants per group (N = 30). A plausible Descriptives table might show:

Levene’s test in this example returns p = .412, which is above .05, so the equal-variances assumption holds and the standard ANOVA and Tukey HSD output can be interpreted directly.

Step 4: Read the ANOVA table

The main ANOVA summary table reports Sum of Squares, degrees of freedom, Mean Square, F, and Sig. (the p-value) for Between Groups, Within Groups, and Total:

Degrees of freedom follow directly from group and sample sizes: df_between = k − 1 (number of groups minus 1, here 3 − 1 = 2), df_within = N − k (total sample size minus number of groups, here 30 − 3 = 27), and df_total = N − 1 (29). F is the ratio of Mean Square Between to Mean Square Within (122.80 / 26.98 = 4.55 in this example). Because Sig. (.020) is below the conventional .05 threshold, this result would be reported as statistically significant — at least one group mean differs from at least one other.

Step 5: Interpret the Tukey post-hoc comparisons

A significant omnibus F tells you a difference exists somewhere among the groups, but not which specific pairs differ. The Tukey HSD (Honestly Significant Difference) test, requested in Step 2, controls the family-wise error rate across all pairwise comparisons — this matters because running three uncorrected t-tests instead would inflate your Type I error rate.

In the Multiple Comparisons table, SPSS lists every pairwise comparison with a mean difference, standard error, and Sig. value. For the illustrative example above, a plausible pattern is:

• A vs. C: mean difference significant, p = .015 — spaced practice outperforms no structured method.
• A vs. B: mean difference not significant, p = .089 — spaced and massed practice don’t differ reliably at the .05 level, though the trend favours A.
• B vs. C: mean difference not significant, p = .612 — massed practice and no structured method don’t differ reliably.

This pattern is common with a significant but modest omnibus F: only the two most extreme groups reach significance in post-hoc testing, even though the overall test was significant. Students often misread this as “the ANOVA was significant, so I can just describe all three groups as different” — always check the specific post-hoc comparisons before making claims about any individual pair.

Step 6: Calculate and report effect size

SPSS’s standard One-Way ANOVA procedure doesn’t automatically output eta squared in older versions, though newer versions can via the Effect Size option under Options. You can calculate it directly from the ANOVA table: eta squared (η²) equals SS_between divided by SS_total. In the example: 245.60 / 974.00 = 0.252, or η² = .25.

By convention (Cohen, 1988), η² values of approximately .01, .06, and .14 correspond to small, medium, and large effects respectively, so .25 in this illustrative example would be interpreted as a large effect. Note that when the ANOVA is embedded in a General Linear Model procedure rather than the simple One-Way ANOVA dialog, SPSS labels this statistic partial eta squared (partial η²) — for a one-way design with a single factor, the two are numerically identical.

Step 7: Write it up in APA 7 format

The standard APA 7 template for a one-way ANOVA result is:

F(df_between, df_within) = X.XX, p = .XXX, η² = .XX

Applied to the illustrative example, a full results paragraph would read:

A one-way ANOVA was conducted to compare the effect of study method on exam score across three conditions (spaced practice, massed practice, and no structured method). There was a statistically significant effect of study method on exam score, F(2, 27) = 4.55, p = .020, η² = .25. Post hoc comparisons using the Tukey HSD test indicated that the mean score for the spaced practice group (M = 78.4, SD = 6.2) was significantly higher than the no-structured-method group (M = 68.9, SD = 8.5), p = .015. The massed practice group (M = 71.1, SD = 7.8) did not differ significantly from either the spaced practice group (p = .089) or the no-structured-method group (p = .612).

Note the formatting conventions: italicize F, p, M, and SD; report p-values to three decimal places without a leading zero (.020, not 0.020); and always report degrees of freedom in parentheses immediately after F. If reporting an exact p-value below .001, APA 7 convention is to write p < .001 rather than the exact figure SPSS displays.

What if your assumptions are violated

If Levene’s test is significant (unequal variances), SPSS’s One-Way ANOVA Options dialog offers a Welch’s F correction, which adjusts the degrees of freedom to account for unequal variances and should be reported instead of the standard F. If your Tukey post-hoc comparisons are being run alongside unequal variances, switch to the Games-Howell post-hoc test instead of Tukey, which doesn’t assume equal variances. If normality is severely violated and your sample per group is small, consider the non-parametric Kruskal-Wallis H test as an alternative to ANOVA entirely — it compares mean ranks rather than means and doesn’t require the normality assumption.

If your design involves more than one grouping variable, or the same participants measured under different conditions, you need a different test entirely — a factorial ANOVA or repeated-measures ANOVA respectively — which fall outside a one-way design. Similarly, if your outcome variable is continuous but your independent variables are also continuous predictors rather than categorical groups, you likely need our guide to running a multiple regression in SPSS and reporting it in APA instead. If your dependent variable is a multi-item scale, check its internal consistency first with our guide to calculating Cronbach’s alpha in SPSS before running any group comparison on it.

Common mistakes to avoid

• Running multiple independent t-tests instead of one ANOVA. Comparing three groups with three separate t-tests inflates the family-wise Type I error rate well above the nominal .05 level. Use ANOVA with a proper post-hoc correction instead.
• Skipping the post-hoc test after a significant omnibus F. A significant ANOVA only establishes that a difference exists somewhere; without post-hoc comparisons you cannot claim any specific pair of groups differs.
• Reporting Tukey results when Levene’s test was significant. Tukey HSD assumes equal variances. If that assumption is violated, Games-Howell is the appropriate correction, not Tukey.
• Confusing statistical significance with practical significance. A large sample can produce a significant p-value even for a trivially small effect. Always report and interpret the effect size (η²) alongside the p-value, not instead of it.
• Forgetting to report degrees of freedom. APA 7 requires both df_between and df_within in parentheses immediately after F — omitting them is one of the most common formatting errors examiners flag.

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