Calculator Form
Example Data Table
| Group | Observation 1 | Observation 2 | Observation 3 | Observation 4 | Observation 5 |
|---|---|---|---|---|---|
| Control | 12 | 15 | 14 | 13 | 16 |
| Campaign A | 18 | 17 | 20 | 19 | 21 |
| Campaign B | 14 | 13 | 15 | 16 | 14 |
| Campaign C | 22 | 24 | 23 | 25 | 21 |
Formula Used
One-way ANOVA separates total variation into between-group variation and within-group variation.
Grand Mean = (Sum of all observations) / N
SS_between = Σ ni(x̄i − x̄)2
SS_within = Σ Σ (xij − x̄i)2
SS_total = SS_between + SS_within
MS_between = SS_between / (k − 1)
MS_within = SS_within / (N − k)
F = MS_between / MS_within
If the p-value is less than alpha, the null hypothesis of equal group means is rejected.
How to Use This Calculator
- Enter a study name if you want a labeled output.
- Set the significance level and preferred decimal precision.
- Choose a chart style and optional group sorting rule.
- Paste one labeled group per line into the data field.
- Click Generate ANOVA Table to compute the test.
- Review the ANOVA table, group summary, interpretation, and Plotly graph.
- Use the CSV or PDF buttons to export the results.
Frequently Asked Questions
1. What does this ANOVA table generator calculate?
It calculates the complete one-way ANOVA table, including sums of squares, degrees of freedom, mean squares, F statistic, p-value, group summaries, and optional effect sizes.
2. What input format should I use?
Enter one group per line. Add a group label, then a colon, then numeric values separated by commas or spaces. Example: Group A: 10, 12, 15.
3. Can groups have different sample sizes?
Yes. The calculator supports unequal group sizes, as long as each group contains at least two observations and the total number of observations exceeds the number of groups.
4. How should I interpret the p-value?
Compare the p-value with alpha. If p is smaller, at least one group mean is statistically different. If not, the evidence is insufficient to claim a meaningful difference.
5. What is the difference between the chart options?
The mean bar chart highlights group averages and standard deviations. The box plot shows distribution spread, median location, and potential outliers for each group.
6. What assumptions does one-way ANOVA make?
One-way ANOVA assumes independent observations, approximately normal data within each group, and reasonably similar group variances. Severe violations can affect the reliability of the test.
7. What do eta squared and omega squared mean?
They are effect sizes. Eta squared shows the share of variance explained by group differences. Omega squared is more conservative and often preferred for practical interpretation.
8. Why might the calculator return an error?
Errors usually happen when groups contain text, missing values, too few observations, or only one valid group. Review the formatting and confirm every entered value is numeric.