Calculator
Select an input mode. Then enter ANOVA values and press Calculate.
Example data table
A sample one-way ANOVA summary. Paste these into the SS mode fields to test.
| Source | SS | df | MS | F |
|---|---|---|---|---|
| Effect (between groups) | 120.50 | 2 | 60.25 | 3.39 |
| Error (within groups) | 480.20 | 27 | 17.79 | — |
| Total | 600.70 | 29 | — | — |
Formula used
- Eta squared: η² = SSeffect / SStotal
- Partial eta squared: partial η² = SSeffect / (SSeffect + SSerror)
- Partial eta squared from F: partial η² = (F · dfeffect) / (F · dfeffect + dferror)
- Omega squared (one-way): ω² = (SSeffect − dfeffect · MSerror) / (SStotal + MSerror)
- Mean squares: MS = SS / df
- F statistic: F = MSeffect / MSerror
- Cohen’s f: f = √(partial η² / (1 − partial η²))
How to use this calculator
- Choose Sums of squares for η² and ω² reporting.
- Enter SS and df from your ANOVA table for the target effect.
- Alternatively choose F statistic when you only have F and df.
- Press Calculate to show effect sizes above the form.
- Use CSV for spreadsheets and PDF for sharing in reports.
- Always interpret magnitudes with domain and study design.
FAQs
1) Which effect size should I report for ANOVA?
Use partial η² for specific effects in factorial models. Use η² for one-way designs with a clear total. Consider ω² when you want a less biased estimate in small samples.
2) Why can omega squared be negative?
ω² subtracts a bias term based on MS(error). With weak effects or small samples, the estimate can dip slightly below zero. Many authors report zero in that case, but also note the raw value.
3) Is partial η² the same as η²?
Not always. In one-way ANOVA, they are identical when SS(total) equals SS(effect)+SS(error). In multi-factor ANOVA, partial η² excludes variance explained by other terms.
4) Can I compute effect size using only F and degrees of freedom?
Yes. Partial η² can be computed from F, df(effect), and df(error). This is helpful when papers provide the test statistic but not the full sums of squares table.
5) What is Cohen’s f used for?
Cohen’s f expresses ANOVA effect magnitude on a scale often used in power analysis. It is derived from partial η². f values near 0.10, 0.25, and 0.40 are common reference points.
6) Should I use corrected or uncorrected SS?
Use the sums of squares from the ANOVA output you report. For unbalanced designs, the SS type (I, II, III) affects partial η². Stay consistent and state the SS type in your methods.
7) Does this calculator replace assumptions checks?
No. Effect size complements significance tests. Still assess independence, residual normality, and variance homogeneity. If assumptions fail, consider robust ANOVA, transformations, or nonparametric alternatives.
8) How should I write an effect size statement?
A typical statement is: “The group effect was moderate, partial η² = 0.08.” Add the test and df when relevant. If you report ω², clarify whether you clamped negatives to zero.