One-way ANOVA
Compare the means of three or more independent groups.
When to use it
Use one-way ANOVA when a numeric outcome might differ across three or more separate groups. For example: do exam scores differ between lecture, online, and workshop teaching? The test asks whether the group means are all the same. It does not, by itself, say which pair differs. That is what a post-hoc test is for.
Two groups only: use the independent-samples t-test.
Assumptions
Scores are numeric, and each person is in one group. Within each group, scores should be roughly normal, and the groups should have similar spread.
Tensr stores Levene’s test on the result. The default is the median-centre version. You can switch it to Brown–Forsythe or turn it off. Levene’s p below .05 means the spreads differ. This procedure does not print a Shapiro–Wilk table. If the spreads differ, use Welch (use_welch, off by default) or the Kruskal–Wallis test.
Running it in Tensr
Options
Prop
Type
Reading the output
The same 96 students, 32 in each teaching method. Tukey compares the pairs. The method gap was built to be a few exam points against a within-group spread of about 8 points.
| Group | n | Mean | Status |
|---|---|---|---|
| Lecture | 32 | 68.209 | included |
| Online | 32 | 72.234 | included |
| Workshop | 32 | 73.741 | included |
| Source | SS | df | MS | F | p | η² |
|---|---|---|---|---|---|---|
| Between Groups | 523.351 | 2 | 261.675 | 4.033 | .021 | 0.08 |
| Within Groups | 6,034.437 | 93 | 64.886 | — | — | — |
| Total | 6,557.787 | 95 |
One-way ANOVA: score by method (3 groups, n = 96). F = 4.033, p = .021 — significant at α = 0.05. Post-hoc: tukey_hsd. The primary result is significant (p = .021). This is large enough, in this sample, to treat the comparison this page is about as a real association rather than noise. Metrics: F statistic = 4.033; p-value = .021; eta squared = 0.08.
Reporting (APA 7)
One-way ANOVA: score by method (3 groups, n = 96). F = 4.033, p = .021 — significant at α = 0.05. Post-hoc: tukey_hsd. This result is significant (p = .021). The effect is moderate, so report its size with the p-value.
Coming from SPSS
Analyze → Compare Means → One-Way ANOVA.
SPSS puts Welch and the post-hoc tests in the same dialog. Tensr’s Welch switch is use_welch, and post hoc is post_hoc. SPSS Options also offers a means plot. Tensr’s chart control is output_chart (boxplot, means_plot, or none).
Related
The rank alternative is the Kruskal–Wallis H test. Two groups: independent-samples t-test. A second factor: two-way ANOVA. A covariate: ANCOVA.