# Effect Size Calculator

Cohen's d, Cohen's h, Phi(φ), Cramer's V, R squared, Eta squared.

You may go to t-test calculator.

## Effect Size Calculator

Effect size measures the magnitude of a statistical phenomenon.
The calculator calculates the effect size. If you have raw data use the Statistic Kingdom test calculators to calculate the p-value and the observed effect size.

1. You should choose one of the following effect size calculators, simply by changing the effect type:
Cohen's d - two-sample equal sd - Cohen's d effect size calculator for the t-test with equal standard deviation.
Cohen's d - two-sample unequal sd - Cohen's d effect size calculator for the t-test with unequal standard deviation.
Cohen's d - one-sample - Cohen's d calculator for the one-sample t-test.
Cohen's h - effect size calculator for two proportion z-test.
Phi (φ) - effect size calculator for the goodness of fit test.
Cramér's V (φ꜀) - effect size calculator for the independence (association) test.
R², and f² - effect size calculator for the linear regression.
η², and f² - effect size calculator for the ANOVA test.
R² to f² - calculate the R-squared from f-squared.
f² to R² - calculate the f-squared from R-squared.
2. Choose "rounding" - When the number is bigger than one the calculator rounds to the required decimal places, but when the number is smaller than one, it rounds to the required significant figures For example, when you choose 2, it will format 88.1234 to 88.12 , and 0.001234 to 0.0012.
3. Enter the relevant input data. If you have raw dat you may go to the relevant test calculator. The test calculator will calculate the summarized data and the observed effect size.
4. Keep the 'Step by step' button on for calculation steps.
5. Press the 'Calculate' button to get the results.

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

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

#### Cohen's d formula

 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.

#### Cohen's h formula

h = 2(arcsin(√p1) - arcsin(√p2))

### Phi effect size

The Phi(φ) effect size is use for the chi-squared test - goodness of fit.
n - sample size.
χ - the chi-squared test statistic.

#### Phi effect formula

 φ = √ χ2 n χ2 = Σ (oi - ei)2 ei

### Cramer's V effect size

The Cramer's V effect size is use for the chi-squared test - Independence (Association).
n - sample size.
χ - the chi-squared test statistic.
R - number of rows.
C - number of columns.

#### Cramer's V formula

 V = √ χ2 n*Min(R - 1, C - 1)

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

The R-Squared for the linear 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.

#### Linear regression effect size formula

 R2 = SSR SST

#### ANOVA effect size formula

 η2 = SSG SST

SSR - sum of squares of the regression.
SSG - sum of squares between the group.
SST - total sum of squares.

#### f-square from R-square formula

 f2 = R2 1 - R2

#### R-square from f-square formula

 R2 = f2 1 + f2