Calculate Effect Size From T-Value and N

Effect size is a measure of the strength of a relationship or difference between groups in a study. It helps researchers understand the practical significance of their findings beyond just statistical significance. This calculator helps you determine the effect size from a t-value and sample size (n).

What is Effect Size?

Effect size is a standardized measure that quantifies the magnitude of a phenomenon. In statistics, it helps distinguish between a meaningful difference and a trivial one. Common effect size measures include Cohen's d for independent samples, Pearson's r for correlation, and Hedges' g for meta-analysis.

Effect size is different from statistical significance. A result can be statistically significant (p < 0.05) but have a small effect size, meaning the difference is not practically important.

How to Calculate Effect Size

The most common method to calculate effect size from a t-value and sample size is to use Cohen's d formula:

Effect Size (d) = t / √(n)

Where:

t is the t-value from your statistical test
n is the sample size (number of observations)

This formula assumes you have a one-sample t-test. For independent samples (two groups), the formula is slightly different:

Effect Size (d) = t / √(n₁ + n₂)

Where:

t is the t-value from your independent samples t-test
n₁ is the sample size of group 1
n₂ is the sample size of group 2

For paired samples, the formula is the same as for one-sample t-tests.

Interpreting Effect Size

Effect size values are interpreted based on conventions established by Jacob Cohen in 1988:

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

These benchmarks are general guidelines and may vary depending on the field of study. Always consider the context of your research when interpreting effect sizes.

Effect size should be reported alongside statistical significance (p-value) for a complete picture of your results.

Worked Example

Let's say you conducted a one-sample t-test comparing the average height of a sample to a known population average. You found a t-value of 2.5 with a sample size of 36.

Using the formula:

Effect Size (d) = 2.5 / √36 = 2.5 / 6 = 0.4167

This is a medium effect size (0.5 ≤ d < 0.8), indicating a meaningful difference in height between your sample and the population.

FAQ

What is the difference between effect size and p-value?

A p-value tells you whether a result is statistically significant, while effect size tells you how large or important that result is. A small p-value with a large effect size is more meaningful than a small p-value with a small effect size.

Can I calculate effect size from a correlation coefficient?

Yes, the effect size for a correlation is simply the absolute value of the correlation coefficient (r). For example, if you have r = 0.6, the effect size is 0.6.

What if my sample size is very small?

With small sample sizes, effect sizes can be unstable and unreliable. Always consider the sample size when interpreting effect sizes. Larger samples provide more stable and generalizable effect size estimates.

How do I report effect size in my research paper?

Effect sizes should be reported with their confidence intervals and effect size measures (like Cohen's d). For example: "The effect size was d = 0.42 (95% CI: 0.21 to 0.63)."