Enter ANOVA Error Terms and Group Means
Use balanced or unbalanced sample sizes for pairwise Scheffe comparisons.
Example Data Table
This example uses four teaching methods with the same ANOVA error term.
| Group | Mean | Sample Size |
|---|---|---|
| Method A | 78.4 | 8 |
| Method B | 82.1 | 8 |
| Method C | 88.0 | 8 |
| Method D | 80.2 | 8 |
Use MSE = 4.2, error df = 20, and α = 0.05.
Formula Used
Scheffe testing compares every mean pair after a significant ANOVA. For groups i and j, the standard error is:
SE = √[ MSE × (1/ni + 1/nj) ]
The Scheffe critical difference for a pairwise comparison is:
CD = √[ (k − 1) × Fα, k−1, df_error × MSE × (1/ni + 1/nj) ]
The pairwise test statistic is:
F = (Mean Difference)2 / [ (k − 1) × MSE × (1/ni + 1/nj) ]
If the absolute mean difference exceeds the critical difference, that pair is significant at the chosen alpha level.
How to Use This Calculator
- Enter your ANOVA significance level, MSE, and error degrees of freedom.
- Set the number of groups, then build the input rows.
- Type each group name, sample mean, and sample size.
- Press the calculate button to generate all pairwise Scheffe comparisons.
- Review the significant pairs, then export the table as CSV or PDF.
FAQs
1. What does the Scheffe test do?
It checks which group means differ after ANOVA. It controls familywise error conservatively, making it useful when many comparisons are possible.
2. When should I use Scheffe instead of Tukey?
Use Scheffe when you want strong protection against false positives or when you may test many contrasts, not only simple pairwise comparisons.
3. Can this calculator handle unequal sample sizes?
Yes. Each pairwise standard error uses the entered sample sizes directly, so unbalanced group designs are supported.
4. Do I need a significant ANOVA first?
Usually yes. Post hoc procedures are normally interpreted after the overall ANOVA indicates that at least one mean differs somewhere.
5. What inputs come from my ANOVA table?
You need the mean square error, the error degrees of freedom, and the number of groups. Then add the group means and sample sizes.
6. Why is Scheffe considered conservative?
Its threshold is stricter than many alternatives. That lowers false positives, but it can also reduce power for small differences.
7. What does the critical difference mean?
It is the minimum gap between two means required for significance. Larger observed differences are flagged as statistically significant.
8. Can I export results for reports?
Yes. Use the built-in CSV option for spreadsheets and the PDF option for clean report sharing or archiving.