Effect size calculator
A p-value tells you whether an effect is there; an effect size tells you how big it is. This calculates the ones a dissertation reports.
An effect size quantifies the magnitude of a result on a scale that does not depend on the sample size, which is why reviewers now expect one beside every significance test. This calculator returns Cohen's d and the bias-corrected Hedges' g from two groups' means, eta-squared from an ANOVA F, and the odds ratio and risk ratio from a 2x2 table, including the conversion between them. Each comes with the formula it was computed from.
Cohen's d
0.666
A medium effect by Cohen's benchmarks.
The formulas behind each effect size
Cohen's d standardises the difference between two means by the pooled standard deviation:
d = (M₁ - M₂) / s_pooled
Hedges' g multiplies d by a small-sample correction factor, J = 1 - 3 / (4 × df - 1), which removes the upward bias d carries in small samples. Eta-squared from an F statistic is:
η² = (df₁ × F) / (df₁ × F + df₂)
The odds ratio is ad / bc from the 2x2 table, the risk ratio compares the two row risks, and the conversion uses RR = OR / (1 - p₀ + p₀ × OR), where p₀ is the baseline risk. The odds ratio and risk ratio only coincide when the outcome is rare, which is why the baseline risk has to be supplied for the conversion.
Frequently asked questions
- What is the formula for calculating effect size?
The formula depends on the effect size. Cohen's d is the difference between two means divided by their pooled standard deviation, eta-squared is the between-groups sum of squares divided by the total sum of squares, and an odds ratio is the cross-product of a 2x2 table. This calculator computes each of these from the summary figures you enter.
- How do you calculate eta squared?
Eta-squared is the proportion of total variance explained by a factor, calculated as the factor's sum of squares divided by the total sum of squares. When you only have the ANOVA output, it can be recovered from the F value and the degrees of freedom, which is what this tool does. The result ranges from 0 to 1, where 0.01, 0.06, and 0.14 mark small, medium, and large effects.
- How do you convert an odds ratio to a risk ratio?
An odds ratio is converted to a risk ratio using the baseline risk in the unexposed group: RR = OR / (1 - p0 + p0 x OR), where p0 is that baseline risk. The two values diverge as the outcome becomes more common, so the conversion matters most for frequent events. Enter the odds ratio and the baseline risk above to apply this formula.
- Should I use an odds ratio or a risk ratio?
Risk ratios are easier to interpret and are preferred for cohort studies and randomised trials, where the baseline risk is known. Odds ratios suit case-control studies and logistic regression, where risks cannot be estimated directly. For common outcomes the odds ratio overstates the effect, so a risk ratio is the safer summary whenever you can compute it.