Post Hoc ANOVA Calculator

Calculator

Group Data

Put one group per line. Use a label followed by a colon, then values. Commas, spaces, or mixed separators are accepted.

Alpha Level Post Hoc Method Decimal Places

Sort groups by mean before reporting

Advanced Notes

This page runs a one-way ANOVA first. Pairwise tests then use the pooled within-group error term from the ANOVA table.

Best use cases include model evaluation groups, A/B/n experiments, algorithm variants, and treatment-response comparisons.

For very unequal variances or strongly non-normal data, confirm conclusions with a robust or nonparametric workflow.

Example Data Table

This sample uses four groups with five observations each. You can paste the same values into the calculator to test the workflow quickly.

Group	Values	Mean	n
Control	12, 15, 14, 13, 16	14.0	5
Treatment A	18, 17, 19, 20, 18	18.4	5
Treatment B	14, 13, 15, 16, 14	14.4	5
Treatment C	21, 20, 22, 19, 23	21.0	5

Formula Used

Grand Mean: \[ \bar{x}_{grand} = \frac{\sum_{i=1}^{k}\sum_{j=1}^{n_i} x_{ij}}{N} \]

Between-Groups Sum of Squares: \[ SS_B = \sum_{i=1}^{k} n_i (\bar{x}_i - \bar{x}_{grand})^2 \]

Within-Groups Sum of Squares: \[ SS_W = \sum_{i=1}^{k}\sum_{j=1}^{n_i}(x_{ij} - \bar{x}_i)^2 \]

Mean Squares and F Statistic: \[ MS_B = \frac{SS_B}{k-1}, \quad MS_W = \frac{SS_W}{N-k}, \quad F = \frac{MS_B}{MS_W} \]

Pairwise Post Hoc t Statistic: \[ t_{ij} = \frac{\bar{x}_i - \bar{x}_j}{\sqrt{MS_W(\frac{1}{n_i} + \frac{1}{n_j})}} \]

Effect Sizes: \[ \eta^2 = \frac{SS_B}{SS_T}, \quad \omega^2 = \frac{SS_B - (k-1)MS_W}{SS_T + MS_W} \]

The calculator computes raw pairwise p values from the pooled-error t statistic, then adjusts those p values using the selected post hoc method.

How to Use This Calculator

Enter one group per line in the data box. Put the label first, then a colon, then numeric observations.
Choose the significance level α. Common choices are 0.05 or 0.01.
Select a post hoc correction. Holm is a strong general-purpose option for family-wise error control.
Pick the number of decimals and optionally sort groups by their means.
Press Run Post Hoc ANOVA. The page will show the ANOVA summary above the form.
Review the descriptive table, then inspect the pairwise post hoc table for adjusted p values and confidence intervals.
Use the Plotly graph to compare means quickly.
Download CSV for spreadsheet work or PDF for reports and presentations.

FAQs

1) What does this calculator test?

It tests whether at least one group mean differs using one-way ANOVA, then compares pairs of groups with corrected post hoc p values.

2) When should I use Holm instead of Bonferroni?

Holm usually gives more power than Bonferroni while still controlling family-wise error. It is often a better default when you want strict error control.

3) What is Fisher LSD best for?

Fisher LSD is less conservative and can find more differences, but it raises false-positive risk. Use it carefully and mainly for exploratory work.

4) What do eta squared and omega squared mean?

They estimate effect size for the overall ANOVA. Eta squared is more direct, while omega squared is typically less biased for population effects.

5) Can I use unequal sample sizes?

Yes. The calculator supports different group sizes. The pooled-error post hoc tests still assume reasonably similar variances across groups.

6) What if the ANOVA p value is not significant?

You can still inspect pairwise results, but conclusions should be cautious because the overall evidence for mean differences is weak.

7) Does this replace robust or nonparametric analysis?

No. If variances are highly unequal, data are skewed, or outliers dominate, validate findings with a robust alternative.

8) What kinds of projects fit this tool?

It fits experiment analysis, model version comparisons, feature tests, treatment groups, process variants, and other grouped numeric datasets.