Calculate Effect Size From T and N

Effect size measures the magnitude of a phenomenon, such as the difference between two groups in a study. Calculating effect size from a t-statistic and sample size provides a standardized measure of the difference that can be compared across studies.

What is Effect Size?

Effect size is a quantitative measure of the strength of a phenomenon or relationship. In statistics, it helps determine whether an observed difference or relationship is meaningful beyond chance. Common effect size measures include Cohen's d, Hedges' g, and Pearson's r.

Effect size should be interpreted alongside statistical significance. A statistically significant result with a small effect size may not be practically important.

How to Calculate Effect Size from t and n

The most common effect size measure is Cohen's d, which can be calculated from a t-statistic and sample size using the following formula:

d = t / √(n₁ + n₂ - 2)

Where:

d = effect size
t = t-statistic from the study
n₁ = sample size of group 1
n₂ = sample size of group 2

For independent samples, the formula simplifies to:

d = t / √(n - 2)

Where n is the total sample size (n₁ + n₂).

This calculator uses the independent samples formula. For paired samples, a different approach is needed.

Interpreting Effect Size

Effect size values are interpreted using the following guidelines:

Small effect: 0.2 ≤ d < 0.5
Medium effect: 0.5 ≤ d < 0.8
Large effect: d ≥ 0.8

These benchmarks are based on Cohen's original recommendations and are widely used in social sciences. The interpretation may vary slightly depending on the field of study.

Worked Example

Suppose you have a study with a t-statistic of 2.5 and a total sample size of 50 participants. Using the formula:

d = 2.5 / √(50 - 2) = 2.5 / 7.071 = 0.353

This indicates a small effect size (0.2 ≤ 0.353 < 0.5).

FAQ

What is the difference between effect size and statistical significance?

Statistical significance tells you whether an effect is unlikely to have occurred by chance, while effect size tells you how large or important that effect is. A statistically significant result with a small effect size may not be practically meaningful.

Can I calculate effect size from a p-value?

No, p-values only indicate statistical significance, not effect size. You need the t-statistic and sample size to calculate effect size.

What if my study has unequal group sizes?

The formula provided works for both equal and unequal group sizes. The total sample size (n₁ + n₂) is used in the denominator.

How do I report effect size in a paper?

Include the effect size measure (d), its value, and the interpretation (small/medium/large) in your results section. For example: "The effect size was d = 0.42, indicating a medium effect."