How to use
- Paste one column per group. A header row with group names is optional; groups can have different sizes.
- Read F and p. p < 0.05 means at least one group mean differs from the others.
- Check the equal-variance table. If Levene's test is significant, report Welch's ANOVA instead.
- Use the Tukey HSD table to see which pairs differ, and copy the APA line.
Options explained
- η² and ω²
- η² is the between-groups sum of squares divided by the total, the share of variance explained by group. 0.01, 0.06 and 0.14 are the usual small, medium and large benchmarks. ω² corrects η²'s upward bias in small samples.
- Levene's test
- An ANOVA on each value's distance from its group median (the Brown–Forsythe version, more robust to skew). It is the "based on median" row in SPSS.
- Tukey HSD
- Compares every pair of groups with p-values adjusted for the number of comparisons. With unequal group sizes this is the Tukey–Kramer method.
Worked example
The sample data are scores from three groups (A has 6 people, B 5, C 7):
| Group | n | Mean | SD |
|---|---|---|---|
| A | 6 | 4.583 | 0.471 |
| B | 5 | 5.820 | 0.460 |
| C | 7 | 5.243 | 0.516 |
| Source | SS | df | MS | F | p |
|---|---|---|---|---|---|
| Between groups | 4.2115 | 2 | 2.1058 | 8.889 | 0.0028 |
| Within groups | 3.5535 | 15 | 0.2369 | ||
| Total | 7.765 | 17 |
p = 0.0028, so the group means differ, with η² = 0.54. Levene’s test gives p = 0.92, so the variances are similar and the ordinary F test is fine (Welch’s ANOVA agrees: F = 9.07, p = 0.006).
Tukey HSD: A vs B differ by −1.24 (p = 0.002). A vs C (p = 0.068) and B vs C (p = 0.140) are not significant, so the effect comes mainly from A and B.
APA style: F(2, 15) = 8.89, p = .003, η² = .54.
When to use one-way ANOVA
- You compare the means of three or more independent groups, such as test scores from three classes or yields under four fertilizers.
- There is a single grouping factor. Two factors (method × gender) need a two-way ANOVA, which this tool doesn’t do.
- Repeated measurements on the same people (pre, mid, post) are not independent groups; they need repeated-measures ANOVA.
Running several t-tests instead inflates false positives: three pairwise tests at 5% each give close to a 14% chance of at least one false alarm.
Frequently asked questions
Can I use it with two groups?
Yes. One-way ANOVA with two groups is the same as an equal-variance t-test, and F equals t squared. Most people report the t-test in that case.
My ANOVA is significant. What next?
Look at the Tukey HSD table. Pairs with p < 0.05 are the ones that differ. A significant F alone doesn't tell you which groups are different.
What if the data aren't normal?
With 30 or so per group ANOVA is fairly robust. For small, skewed samples or ratings, use the Kruskal–Wallis test in the Mann–Whitney tool.
Does it match SPSS and R?
F, p, Welch and Tukey match R's aov(), oneway.test() and TukeyHSD(). SPSS "One-Way ANOVA" with the homogeneity test (based on median) gives the same numbers.
Is my data uploaded?
No. Everything is calculated in your browser.
Privacy
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