Enter Dataset
Paste long-format data with one row per observation. The default layout expects a group column and one numeric value column.
Example Data Table
This sample mirrors the default dataset and shows the structure expected by the calculator.
| Group | Value |
|---|---|
| Control | 52 |
| Control | 49 |
| Control | 51 |
| Control | 50 |
| Treatment A | 58 |
| Treatment A | 61 |
| Treatment A | 59 |
| Treatment A | 60 |
| Treatment B | 54 |
| Treatment B | 56 |
| Treatment B | 55 |
| Treatment B | 57 |
Formula Used
Group mean: \(\bar{y}_g = \frac{\sum y_{ig}}{n_g}\)
Fitted value: \(\hat{y}_{ig} = \bar{y}_g\)
Residual: \(e_{ig} = y_{ig} - \hat{y}_{ig}\)
Within-group sum of squares: \(SSE = \sum (y_{ig} - \bar{y}_g)^2\)
Mean squared error: \(MSE = \frac{SSE}{N-k}\)
RMSE: \(RMSE = \sqrt{MSE}\)
Leverage for one-way ANOVA: \(h_{ii} = \frac{1}{n_g}\)
Standardized residual: \(r_i = \frac{e_i}{\sqrt{MSE(1-h_{ii})}}\)
F statistic: \(F = \frac{MSB}{MSE}\), where \(MSB = \frac{SSB}{k-1}\)
Effect size: \(\eta^2 = \frac{SSB}{SST}\)
Jarque-Bera screen: \(JB=\frac{n}{6}\left(S^2 + \frac{(K-3)^2}{4}\right)\)
How to Use This Calculator
- Paste your long-format data into the dataset box.
- Choose the correct delimiter for the pasted rows.
- Set the group column and numeric value column positions.
- Keep the header box checked when your first row contains labels.
- Select decimal places, alpha level, and a standardized residual threshold.
- Press Analyze Residuals to place results below the header and above the form.
- Review ANOVA summary metrics, group diagnostics, and observation-level residual flags.
- Inspect the Plotly charts for shape, spread, and unusual points.
- Use the export buttons to save the residual table as CSV or PDF.
FAQs
1. What does this calculator analyze?
It evaluates one-way ANOVA residual behavior. The page computes fitted values, residuals, standardized residuals, ANOVA summary metrics, group spreads, and several visual diagnostics.
2. Why are residuals important after ANOVA?
Residuals show whether model assumptions look reasonable. Patterns, extreme values, and unstable spread can suggest non-normality, unequal variances, data entry issues, or model misspecification.
3. What is a fitted value in one-way ANOVA?
The fitted value is the mean of the observation’s group. Each residual is simply the observed value minus that group average.
4. How should I interpret standardized residuals?
Values near zero are typical. Larger absolute values deserve attention. Many analysts use thresholds near 2 or 3 as practical screening points for unusual observations.
5. Does the calculator prove normality or equal variances?
No. It provides screening evidence, not proof. Use the tables and graphs to support judgment, then combine them with subject knowledge and additional testing when necessary.
6. What does the Jarque-Bera value indicate?
It summarizes skewness and kurtosis in the residuals. Smaller values usually look more normal, while lower p values suggest the residual shape may depart from normality.
7. Can I paste data copied from a spreadsheet?
Yes. Paste long-format rows, choose the correct delimiter, set column positions, and keep the header option aligned with your copied table.
8. What file can I save this page as?
Save the file as anova_residual_analysis.php. That matches the filename referenced in the opening code comment.