can cohen's d be negative

2 min read 11-03-2025

Cohen's d is a frequently used measure of effect size, quantifying the difference between two group means in standardized units. But a question often arises: Can Cohen's d be negative? The short answer is yes, and understanding why is crucial for interpreting effect size calculations correctly.

Understanding Cohen's d

Cohen's d represents the difference between two means (e.g., the mean scores of an experimental group and a control group) divided by a standard deviation (usually the pooled standard deviation of the two groups). This standardization allows for comparison across studies with different scales or units of measurement. A larger absolute value of Cohen's d indicates a stronger effect.

The Significance of the Sign

The sign of Cohen's d (+ or -) indicates the direction of the effect, not whether the effect is "significant" in a statistical sense. A positive Cohen's d means the group represented by the first mean in the calculation has a higher average score than the second group. A negative Cohen's d simply means the opposite: the second group has a higher average score.

Example:

Let's say we're comparing the average test scores of students in two different teaching methods. If Group A (Method 1) has a mean score of 85 and Group B (Method 2) has a mean of 75, and the pooled standard deviation is 10, then Cohen's d would be calculated as:

d = (85 - 75) / 10 = 1.0

This indicates a large effect size, with Method 1 resulting in higher average scores.

However, if Group B had a mean of 85 and Group A had a mean of 75, Cohen's d would be:

d = (75 - 85) / 10 = -1.0

This negative value still indicates a large effect size, but now it shows that Method 2 resulted in higher average scores. The magnitude of the effect remains the same; only the direction has changed.

Interpreting Negative Cohen's d Values

When you encounter a negative Cohen's d, don't be alarmed. It simply reflects the direction of the difference between the means. Focus on the absolute value of Cohen's d to understand the magnitude of the effect. The sign simply helps interpret which group had the higher mean score.

Common Misinterpretations

It's important to avoid misinterpreting a negative Cohen's d as indicating a smaller effect. The negative sign only reflects the direction, not the size, of the effect. A Cohen's d of -1.0 represents the same magnitude of effect as a Cohen's d of +1.0.

Conclusion: The Sign Matters, But Magnitude is Key

A negative Cohen's d is perfectly valid and simply reflects that the second group in your calculation has a higher mean than the first. Pay close attention to the sign to understand the direction of the effect, but prioritize the absolute value to assess the magnitude or strength of the effect. Remember to always clearly state which group's mean was used first in your calculation when reporting your findings. This ensures clear and unambiguous interpretation of your effect size.