In statistics, an effect size tells us how large the difference is between the mean of two groups.

One of the most common measurements of effect size is **Cohen’s d**, which is calculated as:

Cohen’s d = (x_{1} – x_{2}) / √(s_{1}^{2 }+ s_{2}^{2}) / 2

where:

- x
_{1}, x_{2}: mean of sample 1 and sample 2, respectively - s
_{1}^{2}, s_{2}^{2}: variance of sample 1 and sample 2, respectively

Using this formula, here is how we interpret Cohen’s d:

- A
*d*of**0.5**indicates that the two group means differ by 0.5 standard deviations. - A
*d*of**1**indicates that the group means differ by 1 standard deviation. - A
*d*of**2**indicates that the group means differ by 2 standard deviations.

And so on.

We use the following rule of thumb when interpreting Cohen’s d:

- A value of
**0.2**represents a small effect size. - A value of
**0.5**represents a medium effect size. - A value of
**0.8**represents a large effect size.

When reporting the value of Cohen’s d in a final report, you should keep the following in mind:

- Use a lowercase
*d*. - Round Cohen’s d to two decimal places (unless otherwise specified).
- Mention whether the effect size is considered small, medium or large.

The following example shows how to report Cohen’s d in practice.

**Example: How to Report Cohen’s d**

Suppose a mechanical engineer want to know if a new fuel treatment leads to a change in the average miles per gallon of a certain car.

To test this, he conducts an experiment in which 12 cars receive the new fuel treatment and 12 cars do not.

Here is a summary of the miles per gallon for each group:

**Group #1:**

- x
_{1}: 21 - s
_{1}: 2.73

**Group #2:**

- x
_{2}: 22.75 - s
_{2}: 3.25

Here is how to report the results of the independent samples t-test along with the value of Cohen’s d:

A two sample t-test was performed to compare miles per gallon between fuel treatment and no fuel treatment.

There was not a significant difference in miles per gallon between fuel treatment (M = 22.75, SD = 3.25) and no fuel treatment (M = 21, SD = 2.73); t(22) = -1.428, p = .167. The effect size, measured by Cohen’s d, was d = 0.58, indicating a medium effect.

Notice that we included a lowercase *d*, we rounded Cohen’s d to two decimal places, and we mentioned whether the effect size was considered small, medium or large.

**Additional Resources**

The following tutorials provide additional information about Cohen’s d:

How to Calculate Cohen’s d in Excel

How to Calculate Cohen’s d in R

How to Interpret Cohen’s d