One-way ANOVA Calculator with Tukey Post-hoc Test
Compare three or more groups from a CSV or Excel file: ANOVA, Kruskal-Wallis, Tukey HSD, effect size and box plots in one click.
| Diet | Weight |
|---|---|
| A | 12 |
| A | 14 |
| B | 19 |
| B | 21 |
| C | 14 |
| C | 16 |
| … | … |
| Statistic | Value |
|---|---|
| F (2, 6) | 13.19 |
| p-value | 0.006 |
| η² | 0.815 |
| Tukey A–B | p = 0.006 |
One-way ANOVA with effect size and Tukey post-hoc comparisons.
How to Run an ANOVA
A complete guide to configuring your data pipeline.
Step 1: Upload Your Data
Arrange the data with one column of measurements and one column naming the group of each row (for example Diet = A / B / C). If each group is in its own column, use the Ungroup Columns (Unpivot) tool first to convert the table to this layout.
Step 2: Run the Test
The Compare Groups tool opens with One-way ANOVA selected. Choose the value column and the group column and click Run test. For skewed data or small groups, switch to Kruskal-Wallis, the non-parametric alternative.
Step 3: See Which Groups Differ
A significant ANOVA only tells you that at least one group mean differs. The result therefore includes a post-hoc table: Tukey's HSD after ANOVA, or pairwise Mann-Whitney tests with Holm correction after Kruskal-Wallis. Each pair shows the difference and an adjusted p-value, and the box plot shows all groups side by side.
Technical Specifications & FAQ
One-way analysis of variance compares the variation between group means with the variation within groups. The F statistic is their ratio; a large F with a small p-value indicates that the group means are not all equal. Running many separate t-tests instead would inflate the false-positive rate, which is why ANOVA is followed by a post-hoc procedure that controls the family-wise error.
flowingTable uses SciPy's f_oneway and tukey_hsd, whose results match R's aov() and TukeyHSD(). The effect size is reported as η² (eta squared), the proportion of the total variance explained by the groups. A Levene test checks the equal-variance assumption, and a note is shown when it is clearly violated. Up to 30 groups are supported.
Frequently Asked Questions
What is the difference between ANOVA and Kruskal-Wallis?
One-way ANOVA compares group means and assumes roughly normal data with similar variances. Kruskal-Wallis compares the groups using ranks, so it does not assume normality and is less affected by outliers. Use ANOVA for reasonably symmetric data and Kruskal-Wallis for skewed data, ordinal scores or very small groups.
What does Tukey's HSD tell me?
Tukey's honestly significant difference test compares every pair of groups after an ANOVA and adjusts the p-values so that the chance of any false positive across all pairs stays at 5%. A pair with an adjusted p-value below 0.05 differs significantly.
My groups are in separate columns. Can I still run an ANOVA?
Yes. Use the Ungroup Columns (Unpivot) tool to turn the group columns into one 'variable' column and one 'value' column, then run the ANOVA with 'value' as the measurement and 'variable' as the group. Both steps are recorded in your flow, so you can repeat them on a new file.
What does eta squared (η²) mean?
Eta squared is the share of the total variability explained by the grouping. Common rules of thumb label 0.01 as small, 0.06 as medium and 0.14 or more as large. Unlike the p-value, it does not grow just because the sample is large, so it tells you whether a significant difference is also a meaningful one.