Result
Do the group means differ?
- F statistic
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- p-value
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- R-squared
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- Groups
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- Observations
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- Critical F
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Enter data to see the result.
Calculator Library / Statistics
One-Way ANOVA Calculator
Paste the measurements for each group and find out whether the group averages really differ, and which ones. Includes an ANOVA table, an equal-variance check, and Tukey-Kramer comparisons.
Tool
Enter your groups
F = MS between groups ÷ MS within groups
Paste or type the measurements for each group, separated by spaces, commas, or new lines. You can paste a column straight from Excel or Minitab. Each group needs at least two values, and you need two to eight groups.
Everything runs in your browser. Nothing is sent to a server, and entries are not saved between visits. The example is made-up data from the One-Way ANOVA page in Stat Dojo.
Picture
Observations and group means
Instructions
How to use this calculator
- Name each group and paste its measurements. Use the same units in every group.
- Choose the significance level. 0.05 is the usual choice.
- Read the F statistic and p-value. If p is below alpha, at least one group mean differs.
- Check the assumption panel. A very different spread between groups means you should use Welch’s ANOVA instead.
- Use the Tukey-Kramer table to see which pairs differ. A pair is significant when its interval excludes zero.
- Copy the results into your report, and add the group means and the size of the differences, not only the p-value.
What This One-Way ANOVA Calculator Does
Enter the measurements for two to eight groups and the calculator runs a one-way analysis of variance. It reports the F statistic, the p-value, R-squared, a full ANOVA table, a check of the equal-variance assumption, and Tukey-Kramer comparisons that show which groups differ.
It is built to match the worked example on the One-Way ANOVA page in Stat Dojo, and its numbers agree with Excel’s Anova: Single Factor and with Minitab’s Stat > ANOVA > One-Way.
How the Calculation Works
| Output | Calculation | What it tells you |
|---|---|---|
| Sum of squares between (SSB) | Σ ni (group mean − grand mean)² | Variation explained by the groups |
| Sum of squares within (SSW) | Σ (value − its group mean)² | Variation within the groups, the noise |
| F statistic | (SSB / (k − 1)) ÷ (SSW / (N − k)) | Signal divided by noise |
| p-value | Upper tail of the F distribution | Chance of an F this large if all means were equal |
| R-squared | SSB ÷ (SSB + SSW) | Share of the variation the groups explain |
| Levene test | ANOVA on absolute deviations from each group median | Tests whether the groups have equal spread |
| Tukey-Kramer | Difference ÷ √(MSW / 2 × (1/ni + 1/nj)) against the studentized range distribution | Which pairs differ, with the overall error held at alpha |
Worked Example
The pre-loaded data are fill weights from three filling heads, six fills each. The calculator gives F(2, 15) = 15.52 and p = 0.0002, with R-squared 67%. The Tukey-Kramer table shows that Head 2 fills about 2.13 g heavier than Head 1 and 1.35 g heavier than Head 3, while Heads 1 and 3 cannot be told apart.
The Levene test gives no sign of unequal spread, and the standard deviations differ by a factor of 1.2, so the equal-variance assumption looks fine. Normality and independence still need checking with a probability plot of the residuals and an understanding of how the fills were collected. The post-hoc page shows how.
Limits and Good Practice
- The calculator tests means of one factor. For two factors and interactions, see Two-Way ANOVA and Interactions.
- It assumes independent observations, roughly normal residuals, and similar spread in each group. It checks spread, not normality or independence.
- If the spread differs a lot between groups, use Welch’s ANOVA (available in Minitab and in R) instead of this test.
- With very small groups, the test has little power. A non-significant result does not show that the means are equal.
- Compare differences with what matters in practice, such as a tolerance, and not only with the p-value.
- Data stays in your browser. It is not stored or sent anywhere, and it is not saved between visits.
One-Way ANOVA Calculator Frequently Asked Questions
What does a significant result mean?
It means the data are unlikely if all the group means were equal, at the significance level you chose. At least one group mean differs. It does not say which groups differ or how much; use the Tukey-Kramer comparisons and the sizes of the differences for that.
How many values do I need in each group?
At least two per group for the calculation to run, but more is better. Five to ten per group can detect large differences. Detecting small differences needs far more, so plan the sample with the Sample Size and Confidence Calculator before collecting data.
Can the groups have different numbers of values?
Yes. The calculator handles unbalanced groups and uses the Tukey-Kramer method for comparisons. Balanced groups make the test more robust to unequal spread, so aim for equal sizes when you can.
What if the groups have different spread?
If the Levene test or the standard deviation ratio shows a large difference in spread, use Welch’s ANOVA with Games-Howell comparisons, which are available in Minitab. Then investigate why one group is more variable, because that can be the real finding.
Is my data stored anywhere?
No. The calculator runs entirely in your browser, nothing is sent to a server, and your entries are not saved when you leave the page.