# Effect Size Calculator

Sample size calculator Test power calculator

Cohen's d, Cohen's h, Cohen's phi(φ), R squared, Eta squared.

## Information

Effect size measures the magnitude of a statistical phenomenon.

The calculator calculates the effect size. If you have raw data, Statistic Kingdom test calculators also calculate the effect size from raw data.
You should choose one of the following calculators, simply by changing the effect type:
Cohen's d effect size calculator, Cohen's h effect size calculator, Cohen's phi effect size calculator, R squared effect size calculator, Eta squared calculator.

### What is Cohen's d effect size?

The difference between the means is divided by the standard deviation.

 d = |μ1 - μ2| σ

Usually, we estimate means (μ) and population standard deviations (σ) using the sample averages (x̄) and sample standard deviation (s)

 d = |x̄1 - x̄2| s

When we assume that the standard deviation of the two groups are equal, we use the pooled standard deviation (s), calculating s from the combined sample of the two groups

 s2= (n1 - 1)s12 + (n2 - 1)s22 n1 + n2 - 2

When we assume that the standard deviation of the two groups are not equal, we use the average variance to calculate the standard deviation (s)

 s2= s12+s22 2

### What is h effect size?

When comparing the effect size of the proportion test, the obvious effect size will be the difference p1 minus p2.
But in this case, the power will not be the same for every pair of proportions with the same difference, for example, the power for p1=0.2 and p1=0.3 is not the same as the power for p1=0.3 and p1=0.4.

h = 2(arcsin√p1 - arcsin√p2)

### Cohen's phi effect size

The Cohen's phi(φ) effect size is use for the Chi-squared test for goodness of Fit

 φ = √ χ2 n

### R-Squared/Eta-squared effect size

The R-Squared for the regression model or the Eta-squared for the ANOVA measures the effectiveness of the model. It is the ratio of the variance explained by the model from the total variance of the dependent variable. For a "perfect model", the model explains all the variance, and the effect size is one.
R2 = SSR / SST
η2 = SSG / SST
SSR - sum of squares of the regression.
SSG - sum of squares between the group.
SST - total sum of squares.