Calculator Input
Example Data Table
| Group | Observations | Count | Mean |
|---|---|---|---|
| Model A | 23, 25, 26, 29, 31 | 5 | 26.80 |
| Model B | 20, 21, 22, 24 | 4 | 21.75 |
| Model C | 28, 30, 31, 34, 36, 37 | 6 | 32.67 |
This example uses unequal sample sizes, making it a practical case for one-way ANOVA with weighted grand mean calculations.
Formula Used
This calculator performs a one-way ANOVA for unequal group sizes. It uses the weighted grand mean across all observations.
Grand Mean: \( \bar{x}_{grand} = \frac{\sum n_i \bar{x}_i}{\sum n_i} \)
Between-Groups Sum of Squares: \( SS_B = \sum n_i(\bar{x}_i - \bar{x}_{grand})^2 \)
Within-Groups Sum of Squares: \( SS_W = \sum (n_i - 1)s_i^2 \)
Mean Squares: \( MS_B = \frac{SS_B}{k - 1}, \quad MS_W = \frac{SS_W}{N - k} \)
F Statistic: \( F = \frac{MS_B}{MS_W} \)
The page also calculates eta squared, omega squared, Cohen’s f, Brown-Forsythe variance testing, and pairwise Welch comparisons with Bonferroni control.
How to Use This Calculator
- Enter a significance level, such as 0.05.
- Add at least two groups.
- Type a label for each group.
- Paste numeric values into each group box.
- Separate values with commas, spaces, or new lines.
- Click Run Unbalanced ANOVA.
- Review the ANOVA table, effect sizes, charts, and pairwise tests.
- Use the export buttons to save CSV or PDF output.
8 FAQs
1) What does unbalanced ANOVA mean?
It means the compared groups do not have equal sample sizes. The test still works, but calculations must use weighted group contributions.
2) When should I use this calculator?
Use it when one categorical factor splits data into two or more groups, and each group contains a different number of observations.
3) Can I paste values from a spreadsheet?
Yes. Paste values using commas, spaces, or line breaks. The parser extracts numeric entries and ignores blank separators.
4) Why does the calculator include Brown-Forsythe?
Brown-Forsythe checks whether group spreads differ meaningfully. It is useful because unequal sample sizes can magnify variance imbalance problems.
5) What does eta squared show?
Eta squared estimates the share of total variation explained by the grouping factor. Larger values indicate stronger group separation.
6) Why are pairwise Welch tests included?
ANOVA shows whether any mean differs overall. Welch pairwise tests help identify which pairs differ, while handling unequal variances better than basic pooled tests.
7) What should I do if p is significant?
Review effect sizes, group summaries, and pairwise results. Statistical significance alone does not confirm practical importance.
8) Does unequal sample size always cause problems?
Not always. Problems rise when imbalance combines with large variance differences or strong non-normality. That is why assumption checks matter.