Which post hoc test should I use after ANOVA in SPSS?

When Levene's test shows equal variances, Tukey's HSD is the standard choice and Bonferroni suits a few planned comparisons. When variances are unequal, use Games-Howell instead, because Tukey is no longer valid. Requesting both in advance means the correct one is ready whichever way Levene's test falls.

How do you find the effect size for a one-way ANOVA in SPSS?

The One-Way ANOVA dialog does not print one. Compute eta squared as the between-groups sum of squares divided by the total sum of squares from the ANOVA table, or use omega squared for a less biased value on small samples. Alternatively, run the model through General Linear Model Univariate, which reports partial eta squared directly.

What is the difference between a t-test and a one-way ANOVA?

A t-test compares the means of two groups, while a one-way ANOVA compares three or more in a single test that holds the overall error rate. Running several t-tests instead of an ANOVA inflates the false positive rate. With exactly two groups, an ANOVA and a t-test give the same verdict.

How to run a one-way ANOVA in SPSS

Q: How do you run a one-way ANOVA in SPSS?

Open Analyze, then Compare Means, then One-Way ANOVA. Move your continuous outcome into the Dependent List and your grouping variable into Factor. Under Options request descriptives, the homogeneity test, and the Welch test, choose a post hoc test, then click OK and read the F statistic against an alpha of .05.

To run a one-way ANOVA in SPSS, you open Analyze > Compare Means > One-Way ANOVA, place your continuous outcome in the dependent list and your grouping factor in the factor box, request the right post hoc test and robust options, and read the F statistic against an alpha of .05. The analysis that survives examination, though, depends on checking homogeneity of variance, choosing the correct follow-up comparison, and reporting an effect size the ANOVA dialog does not print by default. This guide covers the full workflow.

When a one-way ANOVA is the right test

A one-way analysis of variance compares the means of three or more independent groups on a single continuous outcome, using one categorical independent variable. It answers one question: do any of the group means differ by more than chance would predict? It does not tell you which groups differ, which is the job of post hoc tests. If you only have two groups, a t-test in SPSS is the matching procedure, and the link between the two is explained in ANOVA versus the t-test. With two grouping factors at once, you move to a two-way ANOVA.

The assumptions and how to check them in SPSS

One-way ANOVA assumes the outcome is roughly normally distributed within each group, that the groups share a common variance (homogeneity of variance), and that observations are independent. Check normality with Shapiro-Wilk and Q-Q plots in Explore, ideally on the model residuals. You do not need a separate variance test, because the One-Way ANOVA dialog prints Levene's Test when you tick Homogeneity of variance test under Options. The single most useful habit here is to also tick the Welch and Brown-Forsythe robust tests, because they give a valid F when variances are unequal and save you from an invalid standard ANOVA.

Running the procedure and the syntax to keep

Open Analyze > Compare Means > One-Way ANOVA, move the outcome into Dependent List and the group variable into Factor. Under Options, request Descriptive, Homogeneity of variance test, Welch, Brown-Forsythe, and the Means plot. Under Post Hoc, choose your comparison (see below). The reproducible syntax is:

ONEWAY score BY group
  /STATISTICS DESCRIPTIVES HOMOGENEITY WELCH BROWNFORSYTHE
  /PLOT MEANS
  /POSTHOC=TUKEY GH ALPHA(0.05)
  /MISSING ANALYSIS.

Choosing the right post hoc test

A significant ANOVA only says at least one mean differs, so you need a post hoc test to locate the differences while holding the family-wise error rate. The choice is driven by Levene's result. When variances are equal, Tukey's HSD is the standard, well-powered option; Bonferroni is more conservative and suits a small number of planned comparisons. When variances are unequal, neither is valid, and you read Games-Howell instead, which is why the syntax above requests both Tukey and Games-Howell so the correct one is ready whichever way Levene falls.

Reading the ANOVA output table by table

SPSS returns several tables in order. Descriptives gives the mean, standard deviation, and size per group for your write-up. The Test of Homogeneity of Variances carries Levene's result: above .05 means equal variances and a valid standard ANOVA. The ANOVA table splits variation into Between Groups and Within Groups, giving the F ratio, its degrees of freedom, and the significance. If Levene was significant, ignore that F and read the Robust Tests of Equality of Means table for the Welch F instead. Finally, the Multiple Comparisons table and the homogeneous subsets table show which specific pairs of groups differ. Reading these in sequence is the wider skill in reading SPSS output tables.

Getting an effect size the dialog hides

The One-Way ANOVA procedure does not print an effect size, which is a common reason dissertations lose marks. You can compute eta squared by hand as the between-groups sum of squares divided by the total sum of squares, both of which sit in the ANOVA table. For a less biased figure, omega squared is preferable on smaller samples. Alternatively, run the same model through Analyze > General Linear Model > Univariate, which prints partial eta squared directly when you request it under Options. Whichever route you take, an eta squared effect size belongs beside the F statistic.

Reporting a one-way ANOVA in APA style

Lead with the descriptive statistics, then the omnibus result in the form F(between degrees of freedom, within degrees of freedom) = value, the exact p-value, and the effect size, followed by the post hoc findings. A clean sentence reads: a one-way ANOVA showed a significant effect of teaching method on test score, F(2, 87) = 6.41, p = .003, omega squared = .11; Tukey post hoc comparisons indicated that the blended group scored higher than the lecture group (p = .002). When you relied on the robust test, state that you report the Welch F because Levene's test was significant. The conventions are detailed in the guide to APA statistical reporting.

What to do when the assumptions fail

If normality is badly violated on small groups and a robust ANOVA is not enough, the rank-based alternative is the Kruskal-Wallis test, found under Analyze > Nonparametric Tests, with Dunn's pairwise comparisons as the follow-up. The decision between a parametric ANOVA and its rank-based counterpart is set out in our comparison of parametric and rank-based tests. Reach for it deliberately, report why you switched, and your analysis stays defensible whatever the data look like.