Enter Group Data
Use raw observations for each group. This calculator performs a one-way ANOVA from the entered values.
Example Data Table
This sample dataset is useful for testing the calculator quickly.
| Group | Values | n | Mean |
|---|---|---|---|
| Training A | 12, 15, 14, 11, 13 | 5 | 13.00 |
| Training B | 20, 22, 19, 21, 23 | 5 | 21.00 |
| Training C | 17, 18, 16, 19, 17 | 5 | 17.40 |
Formula Used
This page uses the classic one-way ANOVA framework.
SSB = Σ nᵢ (x̄ᵢ − x̄)²SSW = Σ Σ (xᵢⱼ − x̄ᵢ)²SST = SSB + SSWdf_between = k − 1df_within = N − kMS_between = SSB / df_betweenMS_within = SSW / df_withinF = MS_between / MS_withinp-value = P(Fdf_between, df_within ≥ observed F)How to Use This Calculator
- Choose how many groups you want to compare.
- Enter a label and raw numeric observations for each group.
- Set your significance level and decimal precision.
- Click the calculate button to generate the ANOVA table.
- Review the F statistic, p value, effect sizes, and group summary.
- Use the CSV or PDF buttons to export the displayed results.
Interpretation Notes
Important
A small p value suggests the observed group mean differences are unlikely under the null hypothesis of equal means.
ANOVA detects whether at least one mean differs. It does not identify which specific groups differ.
For detailed pairwise comparisons, use follow-up post hoc tests such as Tukey HSD after a significant ANOVA result.
FAQs
1) What does the p value mean in anova?
The p value measures how compatible your data is with equal group means. A small p value suggests the observed differences are unlikely from random variation alone, so at least one group mean may truly differ.
2) What does ANOVA test?
ANOVA tests whether multiple group means are statistically equal. It compares between-group variation against within-group variation using the F statistic.
3) What is the null hypothesis in one-way ANOVA?
The null hypothesis states that all population group means are equal. The alternative says at least one group mean differs from the others.
4) What does a large F statistic indicate?
A large F statistic means between-group variation is much larger than within-group variation. That pattern often points toward real mean differences across groups.
5) Does a significant ANOVA show which groups differ?
No. A significant ANOVA only shows that at least one mean differs. You need post hoc testing, such as Tukey comparisons, to identify the specific groups.
6) What assumptions should I check first?
Check independence, approximate normality within groups, and similar group variances. Serious assumption violations can make the p value less reliable.
7) What is eta squared?
Eta squared is an effect size. It estimates how much of the total outcome variability is explained by group membership in the ANOVA model.
8) Can this calculator use summary statistics only?
This version uses raw values for each group. Raw data lets the page compute means, sums of squares, p values, and graph details accurately.