Effect Size (Cohen's d) Calculator

You can use this effect size calculator to quickly and easily determine the effect size (Cohen's d) according to the standard deviations and means of pairs of independent groups of the same size.

How to use this calculator:

1. Take each group (Group 1 and Group 2) and input sample means (M₁, M₂) and sample standard deviations (SD₁, SD₂).
2. Click on the "Calculate" button to generate a value for Cohen's d.

Cohen's d effect size: definition and formula

By effect size, we mean the gap between the mean values of two groups in relation to standard deviation. The size of this gap can be described by effect size regardless of whether a given study design is observational or experimental.

Many publications require the Cohen's d to be reported on the basis that Cohen's means of interpreting the size of an effect, which assists in comprehending the difference between two groups, is generally acknowledged as effective. The Cohen's d statistic is calculated by determining the difference between two mean values and dividing it by the population standard deviation, thus:

Effect Size = (M₁ – M₂ ) / SD

SD equals standard deviation.

In situations in which there are similar variances, either group's standard deviation may be employed to calculate Cohen's d. If the variances are not similar, the pooled standard deviation should be employed; this comprises the average from the standard deviations for both groups. The pooled standard deviation comprises the root mean square for the two standard deviations and is calculated thus:

SD_pooled = √[ (SD₁² + SD₂²) / 2 ]

SD₁ equates to the standard deviation for Group 1, with SD₂ being the standard deviation for Group 2.

Cohen's d may be employed only with normal data distributions, and the highest levels of accuracy will be obtained when there is equality between the sizes and standard deviations of the groups.

Conventionally, Cohen's d is categorized thus: effect sizes below 0.2 are regarded as small, 0.3-0.5 are regarded as medium, and 0.8+ is regarded as large.

Cohen's d effect sizes should only be regarded as a guideline; effect sizes should be examined within the research context and information from similar studies/interventions may facilitate this evaluation.

Formulas

Cohen's d = (M₁ – M₂ ) / SD_pooled

Where: M₁ and M₂ are the means for the 1^st and 2^nd groups, SD_pooled is the pooled standard deviation of the two groups.

To convert Cohen's d into a correlation coefficient (r), use the following equation:

r² = d² / (4 + d²)   [Cohen, 1969].