# Cohen's D Calculator

Created by Wei Bin Loo
Reviewed by Rijk de Wet
Last updated: Oct 05, 2023

With this Cohen's D calculator, we help you measure the standardized effect size between two data sets.

We have written this article to help you understand what Cohen's D is and how to calculate Cohen's D for effect size. We will also demonstrate some practical examples to help you understand the concept.

## What is Cohen's D?

Cohen's D is a standardized effect size measure that represents the difference between the means of two groups in terms of standard deviation units. It is calculated by dividing the difference between the means of two groups by the pooled standard deviation.

A positive Cohen's D indicates that the mean of one group is greater than the mean of the other group, while a negative Cohen's D value indicates the opposite.

## How to calculate Cohen's D?

To understand the calculation of Cohen's D for effect size, let's take the following data sets as an example:

• Data set $A = [5, 9, 3, 45, 8]$.
• Data set $B = [8, 9, 12, 15, 7]$.

You can calculate Cohen's D in four steps:

1. Calculate the means of datasets.

The first step is to calculate the means, $\bar{A}$, and $\bar{B}$, of the two datasets. This can be calculated by dividing the sum of the dataset by the number of data points in the dataset, i.e.:

$\footnotesize \qquad \bar{A} = \frac{ \sum_{i=1}^{n_A} a_i }{ n_A } \\[12pt] \qquad \bar{B} = \frac{ \sum_{i=1}^{n_B} b_i }{ n_B }$

where $n_A$ and $n_B$ are the lengths of $A$ and $B$, respectively. For our example, the means are $\bar{A}=14$ and $\bar{B}=10.2$. Check out our mean calculator and average calculator to understand more about this calculation.

1. Compute the standard deviations of datasets.

Now, compute the standard deviation, $s_A$ and $s_B$, for both sampled data sets $A$ and $B$. You can check out our standard deviation calculator to understand more about this calculation, but the formula is:

$\footnotesize \qquad\! s_A = \sqrt{\frac{\sum_{i=1}^{n_A} (a_i - \bar{A})^2}{n_A-1}} \\[12pt] \qquad\! s_B = \sqrt{\frac{\sum_{i=1}^{n_B} (b_i - \bar{B})^2}{n_B-1}}$

Thus, $s_A = 17.4929$ and $s_B = 3.2711$.

1. Calculate the pooled standard deviation.

Next, calculate the pooled standard deviation ($s_p$) using the formula:

$\footnotesize \qquad\! s_p = \sqrt{\frac{(n_A\!-\!1)s_A^2+(n_B\!-\!1)s_B^2}{n_A+n_B-2}}$

For our example, $s_p = 12.5837$.

1. Calculate Cohen's D.

The last step is to calculate Cohen's D using the Cohen's D formula:

$\footnotesize \qquad\! d = (\bar{A} - \bar{B}) / s_p$

For our example, $d = 0.3020$.

## FAQ

### How to interpret Cohen's D?

This is how you can interpret Cohen's D. A Cohen's D of 0.2, 0.5, and 0.8 or higher are considered small, medium, and large effect sizes, respectively.

The larger Cohen's D, the greater the practical significance of the difference between the groups.

### What is Cohen's D for datasets with same means?

Cohen's D will be 0. You can calculate Cohen's D using the Cohen's D formula:

(mean_1 - mean_2) / pooled standard deviation.

### How can I calculate Cohen's D of two datasets?

You can calculate Cohen's D in four steps:

1. Calculate the means of the two datasets.

2. Compute the standard deviations of the datasets.

3. Calculate the pooled standard deviation.

4. Apply the Cohen's D formula:

(mean_1 - mean_2) / pooled standard deviation

### Can Cohen's D be negative?

Yes, Cohen's D can be negative. When the mean of Group A is less than the mean of Group B, the numerator in the formula will be negative.

A negative Cohen's d indicates that the effect size is in the opposite direction of what was predicted or expected.

Wei Bin Loo
Data set A
a₁
a₂
Data set B
b₁
b₂
Cohen's D
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