Calculator
Example Data Table
| Group | Observations | n | Sample Mean |
|---|---|---|---|
| Group A | 12, 15, 14, 13, 16 | 5 | 14.00 |
| Group B | 18, 17, 19, 16, 20 | 5 | 18.00 |
| Group C | 11, 12, 10, 13, 12 | 5 | 11.60 |
This sample is already preloaded into the calculator for quick testing.
Formula Used
One-way ANOVA mean square error:
MSE = SSW / (N - k)
Confidence interval for each group mean:
meani ± t* × √(MSE / ni)
Confidence interval for a mean difference:
(meani - meanj) ± t* × √(MSE × (1/ni + 1/nj))
ANOVA F statistic:
F = MSB / MSE, where MSB = SSB / (k - 1)
This calculator uses the pooled within-group error term from one-way ANOVA. That makes the intervals consistent with the ANOVA model and especially useful when you compare several group means under a shared variance assumption.
When Bonferroni adjustment is selected, the tool narrows the family-wise error rate by using a stricter critical value for pairwise intervals.
How to Use This Calculator
- Enter one group per line in the textarea.
- Add a label, a colon, and the group observations.
- Choose the confidence level you want to report.
- Select unadjusted or Bonferroni-adjusted pairwise intervals.
- Choose the number of decimals for tables and exports.
- Click the calculate button to show results above the form.
- Review the ANOVA table, mean intervals, and pairwise intervals.
- Use the CSV or PDF buttons to save your report.
Interpretation Notes
- Intervals for group means use the pooled ANOVA error term.
- Pairwise intervals that exclude zero indicate a likely mean difference.
- Bonferroni adjustment is safer when many pairwise comparisons are reviewed.
- ANOVA assumes independent observations, roughly normal errors, and similar group variances.
FAQs
1) What does this calculator estimate?
It computes one-way ANOVA results, pooled error variance, confidence intervals for each group mean, and confidence intervals for pairwise mean differences.
2) Why are pooled intervals useful?
They use the common ANOVA error term, so every group is judged on the same noise estimate. That keeps the results aligned with the ANOVA model.
3) What is the Bonferroni option doing?
It adjusts the pairwise critical value to protect against inflated error rates when you inspect several comparisons at once.
4) When is an interval difference significant?
For pairwise mean differences, significance is suggested when the confidence interval does not cross zero.
5) Can the groups have unequal sizes?
Yes. The formulas used here support unequal sample sizes, and the standard errors automatically reflect those differences.
6) Should I still check assumptions?
Yes. ANOVA results are strongest when observations are independent, residuals are reasonably normal, and group variances are not wildly different.
7) What if my p value is not significant?
That suggests the data do not provide strong evidence of a mean difference at your chosen level. The intervals still help describe uncertainty.
8) What do the export buttons save?
CSV export saves the key result tables. PDF export creates a clean report with summary, ANOVA, and pairwise tables for sharing.