In statistics, we often use p-values to determine if there is a statistically significant difference between the mean of two groups.

However, while a p-value can tell us whether or not there is a statistically significant difference between two groups, an effect size can tell us how large this difference actually is.

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.

Here’s another way to interpret cohen’s d: An effect size of 0.5 means the value of the average person in group 1 is 0.5 standard deviations above the average person in group 2.

We often 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.

The easiest way to calculate Cohen’s d in SPSS is to use **Analyze** > **Compare Means and Proportions** > **Independent-Samples T Test**.

**Example: How to Calculate Cohen’s d in SPSS**

Suppose a botanist wants to know if two different fertilizers lead to different average plant growth (in inches).

She decides to apply the first fertilizer to 12 randomly selected plants and the second fertilizer to another 12 randomly selected plants.

The following dataset in SPSS shows the growth for the plants in each group:

Suppose that the botanist would like to calculate Cohen’s d to determine the effect size of the difference between average growth rate between the two fertilizers.

To do so, click the **Analyze** tab, then click **Compare Means and Proportions**, then click **Independent-Samples T Test**:

In the new window that appears, drag the **Growth** variable to the **Test Variable** panel, then drag the Fertilizer variable to the Grouping Variable panel.

Then check the box next to **Estimate effect sizes**.

Then click the **Define Groups** button.

In the new window that appears, type **One** for **Group1** and Two for **Group2**:

Then click **Continue**. Then click **OK**.

The following output will be produced:

The value for Cohen’s d can be seen in the column named **Point Estimate** for the row named **Cohen’s d**.

We can see that the value for Cohen’s d is **0.264**.

We interpret this to mean that the average height of plants that received fertilizer #1 is **0.264** standard deviations greater than the average height of plants that received fertilizer #2.

Recall the rule of thumb that we mentioned earlier for 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.

Based on this rule of thumb, we would interpret this to be a small effect size.

In other words, whether or not there is a statistically significant difference in the mean plant growth between the two fertilizers, the actual difference between the group means is trivial.

**Additional Resources**

The following tutorials offer additional information on effect size and Cohen’s d:

Effect Size: What It Is and Why It Matters

How to Calculate Cohen’s d in Excel

How to Report Cohen’s d