Eta-Squared (Effect Size)
Computes eta-squared (η²), an effect-size measure for analysis of variance, from the F-statistic and the degrees of freedom. While the F-test says whether there's a significant difference between groups, η² says how much of that difference the grouping variable explains — the proportion of total variance attributable to the groups. It's essential for reporting ANOVA results beyond the p-value. Enter the F-statistic and the numerator and denominator degrees of freedom.
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Eta-Squared (Effect Size)
Computes eta-squared (η²), an effect-size measure for analysis of variance, from the F-statistic and the degrees of freedom. While the F-test says whether there's a significant difference between groups, η² says how much of that difference the grouping variable explains — the proportion of total variance attributable to the groups. It's essential for reporting ANOVA results beyond the p-value. Enter the F-statistic and the numerator and denominator degrees of freedom.
How much difference the ANOVA actually found
An ANOVA F-test can scream significance and yet the difference between groups be tiny in practice. The p-value says whether an effect exists; it doesn't say the size of the effect. Eta-squared fills that gap by answering how much of the data's total variation is explained by the split into groups.
The reading is that of a proportion: an η² of 0.3 means 30% of the variability comes from the differences between groups, and the rest is within-group variation. By convention, values around 0.01, 0.06 and 0.14 mark small, medium and large effects. Reporting η² alongside the p-value has become a requirement in much of the scientific literature, precisely to separate significance from relevance.
Enter the F-statistic and the numerator and denominator degrees of freedom, the same ones you already have from running an ANOVA. The tool returns η². Note this F-based version equals the classic η² computed from sums of squares; for more complex designs, there are variants like partial eta-squared.
Related Tools
One-Way ANOVA
Computes one-way analysis of variance (ANOVA), the test that checks whether three or more groups have different means. It decomposes the total variation into between-group and within-group variation, and the ratio between them (the F-statistic) indicates whether the observed differences are larger than would be expected by chance. It's the generalization of the t-test to multiple groups. Enter the groups: values separated by commas, groups separated by semicolons.
Kruskal-Wallis H Test
Computes the Kruskal-Wallis H test, the non-parametric version of ANOVA for comparing three or more independent groups. Just as Mann-Whitney does for two groups, it works with the ranks of the data instead of the raw values, dispensing with the normality assumption. The H statistic approximately follows a chi-square distribution. It's the choice when the data are ordinal or clearly non-normal. Enter the groups: values by comma, groups by semicolon.
One-Sample Variance Test (Chi-Square)
Computes the chi-square test for the variance of a single sample, which checks whether the population variance equals a reference value. It's the dispersion counterpart of the one-sample t-test for the mean. It shows up often in quality control: is a process's variability within the specified limit, or has it increased? The statistic compares the sample variance with the hypothesized one and follows a chi-square distribution. Enter the sample and the hypothesized variance (σ₀²).
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.