Tip: Use the mode that matches the numbers you already have from your t test output.
Why use an effect size calculator for t test results?
A t test tells you whether a difference is statistically significant. Effect size tells you how large that difference is in practical terms. That distinction matters. With a very large sample, even tiny differences can become significant. With a smaller sample, meaningful effects may fail to reach significance. Reporting effect size gives readers real-world context.
This calculator estimates the most common standardized effect sizes for t tests:
- Cohen's d (standardized mean difference)
- Hedges' g (small-sample corrected version of d)
- r equivalent (effect size correlation from t)
What this calculator computes
1) Independent samples from means/SDs/sample sizes
Use this when you have summary statistics for two groups.
Pooled SD: sp = √(((n1−1)s1² + (n2−1)s2²)/(n1+n2−2))
Cohen's d: d = (M1−M2)/sp
2) Independent samples from t and sample sizes
Use this when your output reports t and group sample sizes but not full descriptive stats.
Cohen's d: d = t × √(1/n1 + 1/n2)
3) Paired samples from difference scores
Use this for repeated-measures or pre-post designs when you have mean and SD of difference scores.
Cohen's dz: dz = Mdiff/SDdiff
How to interpret the output
A common rule of thumb for absolute Cohen's d values is:
- 0.00 to 0.19: negligible
- 0.20 to 0.49: small
- 0.50 to 0.79: medium
- 0.80 to 1.19: large
- 1.20 and above: very large
These are conventions, not universal truths. In some fields, a d of 0.20 can be important; in others, larger effects are expected.
When to report Hedges' g instead of Cohen's d
Hedges' g applies a small-sample correction to d. If your sample is modest, g is often preferred in formal write-ups and meta-analyses. This calculator gives both so you can choose based on your reporting standard.
Example reporting language
You can adapt this template for manuscripts, theses, or reports:
"Participants in Group 1 scored higher than Group 2, t(76) = 2.85, p = .006, Cohen's d = 0.65, Hedges' g = 0.64, indicating a medium-to-large effect."
Common mistakes to avoid
- Using significance level (p value) as a substitute for effect size.
- Mixing paired and independent formulas.
- Forgetting sign direction (positive vs. negative d).
- Ignoring sample size correction when n is small.
- Rounding too aggressively before final reporting.
Quick FAQ
Is a negative Cohen's d wrong?
No. The sign only indicates direction (which group mean is higher). Magnitude is based on absolute value.
Can I compare d values across studies?
Yes, cautiously. Compare studies with similar designs, measures, and populations. Meta-analytic methods are best for formal comparisons.
What if my data are not normal?
Consider robust or nonparametric alternatives, but effect size reporting is still important. Match the effect size to your analysis method.
Bottom line
An effect size calculator for t test output helps you move from "Is there a difference?" to "How much difference is there?" Use this tool to compute standardized effects quickly and report results with stronger practical interpretation.