What Is And How To Calculate Cohen’s d?

What is Cohen’s d?

Cohen’s d is a type of effect size between two means. An effect size is a quantitative measure of the magnitude for the difference between two means, in this regard. Cohen’s d values are also known as the standardised mean difference (SMD).

Since the values are standardised, it is possible to compare values between different variables. Further, the use of d values is often applied in meta-analyses to compute pooled effect sizes of different studies.

What is the Cohen’s d formula?

The Cohen’s d formula is actually really simple. Specifically, it is the difference between two means and divided by the pooled standard deviation. The formula for Cohen’s d can be seen below.

Cohen's d formulaTo calculate the pooled SD, the equation is displayed below. But don’t fear, it is not as bad as you may think.

Pooled standard deviation formulaThe components of the formulas are:

  • M1 = The mean of group 1
  • M2 = The mean of group 2
  • SD1 = The standard deviation of group 1
  • SD2 = The standard deviation of group 2

Calculating Cohen’s d by using an example

Now you know the formula, let’s use it in an example.

We want to calculate the Cohen’s d between two groups: male and females. Specifically, a certain protein was quantified in the blood of the two groups. Females had higher levels of the protein (1.062 ± 0.339) than males (0.528 ± 0.382).

Therefore, the four components for the equation are:

  • M1 = 0.528
  • M2 = 1.062
  • SD1 = 0.382
  • SD2 = 0.339

The easiest way to calculate d values is to firstly calculate the pooled standard deviation. Thus, taking these values and entering them into the equation are shown below.

Pooled standard deviation exampleDoing so will give a pooled standard deviation value of 0.361. So, now we can put this value into the Cohen’s d equation along with the two group means. The full equation is displayed below.

Cohen's d examplePlugging all of that into a calculator will give a d value of 1.479.

But what does the d value actually represent? In the next section, I will explain what the values stand for and how to interpret them.

The Cohen’s d online calculator

If you are still struggling to calculate d values by using the formula, we have created a Cohen’s d calculator.

To use the calculator, simply enter the group mean and standard deviation values, and the d effect size will be calculated for you.

How to interpret Cohen’s d effect sizes

Simply, you can think of Cohen’s d values as standard deviations between the two groups.

A value of 1 indicates that the means of the two groups differ by 1 standard deviation. Taking our example from before, a value of 1.479 indicates the mean differences between the male and female groups differ by 1.479 standard deviations, which is quite a large effect as you will see.

What are small, medium and large effect sizes?

After calculating d values, people often state if the effect size is either: small, medium or large. Cohen himself provided a guide for what values should indicate which size in his book. These are presented below. However, the terms may be dependent upon your field of study.

Small: d = 0.2

Small effect sizes are considered too small to be differentiated by the naked eye. Cohen gave the example of a small effect size as, the difference in height between 15- and 16-year-old girls.

Medium: d = 0.5

Medium effect sizes are just larger enough to be seen by the naked eye. Elaborating on this, Cohen explained that the difference in height between 14- and 18-year-old girls would be calculated as a medium effect size.

Large: d = 0.8

Large effect sizes are really obvious differences between groups. Keeping in alignment with Cohen’s examples, he described this size to be observed when comparing 13- and 18-year-old girl heights.

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