effect size calculator t test

What is effect size in a t-test?

In a t-test, the p-value tells you whether the observed difference is statistically detectable, while the effect size tells you how large that difference is in practical, standardized terms. That is why effect size reporting is now expected in most fields, including psychology, education, medicine, and business analytics.

For mean comparisons, the most common metric is Cohen’s d. It expresses the difference between means in units of standard deviation. As a quick intuition:

• d = 0.20 is often described as a small effect,
• d = 0.50 as a medium effect,
• d = 0.80 as a large effect.

These are rough conventions, not strict rules. Context always matters.

Which effect size does this calculator produce?

1) Independent samples from summary statistics

When you have two means, two standard deviations, and sample sizes, this page computes:

• Cohen’s d using pooled SD,
• Hedges’ g (small-sample corrected d),
• an approximate 95% confidence interval for d.

2) Independent samples from t-statistic

If your software output gives t and sample sizes, you can still estimate effect size directly:

• d = t × √(1/n₁ + 1/n₂),
• plus r and η² from t and df.

3) Paired samples from t-statistic

For repeated-measures designs, this tool returns d_z, calculated as:

d_z = t / √n

This is often used when reporting within-subject change magnitude from a paired t-test.

How to use the calculator correctly

1. Select the method that matches your analysis output.
2. Enter all required values with consistent units.
3. Click Calculate Effect Size.
4. Interpret direction (sign) and magnitude (absolute value).

Positive values indicate Group 1 > Group 2 (or post > pre for paired designs, depending on coding). Negative values indicate the opposite direction.

Interpreting your result

Use the sign for direction and the absolute value for size:

• |d| < 0.20: trivial to very small
• 0.20 to 0.49: small
• 0.50 to 0.79: medium
• ≥ 0.80: large

In applied settings, practical significance can matter more than threshold labels. A “small” effect in medicine or policy can still be highly meaningful.

Reporting example (APA-style)

You can report results like this:

Students in the intervention group scored higher than controls, t(58) = 2.31, p = .024, d = 0.60 (Hedges’ g = 0.59), indicating a medium effect.

If paired:

Scores improved from pretest to posttest, t(23) = 3.12, p = .005, d_z = 0.64, suggesting a medium-to-large within-subject effect.

Common mistakes to avoid

• Mixing formulas for independent and paired designs.
• Ignoring sign direction when interpretation depends on which group is coded first.
• Reporting only p-values without effect sizes or confidence intervals.
• Using raw mean differences only when scales differ across studies.

Final takeaway

A t-test answers, “Is there evidence of a difference?” Effect size answers, “How big is the difference?” You need both for strong statistical reporting. Use the calculator above to quickly compute the most common effect size metrics for t-tests and include them in your results section with confidence.