Calculate Cohen’s d effect size from two groups’ means, standard deviations and sample sizes, or enter raw data for each group instead.

Independent groups only. The signed difference is Group 1 − Group 2; use the same measurement units for both groups. This effect size does not establish statistical or practical significance.

Correction and display

Uses the sample-size-based approximation J ≈ 1 − 3/(4df − 1).

Cohen’s D Calculator

The main method uses the sample-size-weighted pooled sample standard deviation for independent groups. The sign is Group 1 minus Group 2. Raw-data mode computes each group’s sample mean and SD before applying the same formula.

Cd = (M1 − M2) / Sp
Sp = √(((n1 − 1)S1² + (n2 − 1)S2²) / (n1 + n2 − 2))
  • Where Cd is Cohen’s D
  • M2 and M1 are the means
  • S1 and S2 are the standard deviations
  • Sp is the weighted pooled sample SD; n1 and n2 are the sample sizes. The equally weighted two-SD option instead uses √((S1² + S2²)/2), which agrees when sample sizes are equal. One-SD mode uses the supplied reference SD directly.

Cohen’s D Definition

Cohen’s d is a statistical measure used to quantify the effect size of the difference between two groups. It indicates the standardized difference between the means of two groups, considering the variability within each group.

Cohen’s d is valuable as it allows researchers to determine the magnitude of an effect beyond statistical significance, providing a meaningful understanding of the practical significance.

Cohen’s d is important because it helps researchers interpret the practical significance of their findings. Statistical significance alone merely indicates whether the observed difference between two groups is likely to have occurred by chance or not.

By calculating Cohen’s d, researchers can determine the extent to which a difference exists between groups.

A larger absolute d indicates a larger standardized mean difference under the selected SD convention. The sign gives direction. Practical importance depends on the subject and measurement scale; the conventional 0.2, 0.5 and 0.8 reference points are not universal quality thresholds. Optional Hedges g uses J ≈ 1 − 3/(4df − 1), with df = n1 + n2 − 2; this is an approximation rather than the exact gamma-function correction.

Cohen’s D Example

How to calculate Cohen’s D

  1. First, determine the means

    Calculate the means of each data set using a standard formula for averages.

  2. Next, determine the standard deviations

    Calculate the standard deviations, s1 and s2, of each data set.

  3. Calculate the pooled standard deviation

    Using s1 and s2, calculate the pooled standard deviation of the set.

  4. Finally, calculate Cohen’s D

    Using the means from step 1 and the pooled standard deviation, calculate the Cohen’s d.

FAQ

What is Cohen’s D?

Cohen’s d standardizes a mean difference for independent groups. Equal sample sizes are not required for the weighted pooled-SD method; the chosen SD convention and study design affect interpretation.

What is standard deviation?

Sample standard deviation is the square root of the sum of squared deviations from the sample mean divided by n − 1.