Calculator
Formula Used
Effect size r: r = t / √(t² + df)
Eta squared: η² = t² / (t² + df)
Independent groups Cohen's d: d = t × √(1/n1 + 1/n2)
Paired or one sample Cohen's d: d = t / √n
Hedges' g: g = d × correction factor
Equivalent F value: F = t²
How to Use This Calculator
- Enter the reported t statistic from your test.
- Enter the degrees of freedom from the same result.
- Select the correct test design.
- Enter group sample sizes or paired sample size.
- Select the confidence level for the interval estimate.
- Click the calculate button.
- Review Cohen's d, Hedges' g, r, and eta squared.
- Use the CSV or PDF button to save the result.
Example Data Table
| Study | t Value | df | Design | n1 | n2 | Estimated Result |
|---|---|---|---|---|---|---|
| Memory score | 2.45 | 58 | Independent | 30 | 30 | Small to medium effect |
| Reaction time | 3.10 | 24 | Paired | N/A | N/A | Medium effect |
| Survey rating | 1.80 | 72 | Independent | 37 | 37 | Small effect |
Understanding Effect Size From a T Test
What This Calculator Measures
A t test can show whether a difference is statistically clear. It does not show how large that difference is. This calculator fills that gap. It converts the t value into practical effect size measures. These measures help readers judge real importance. They are useful in reports, papers, reviews, and research summaries.
Why Effect Size Matters
A small p value can happen with a large sample. It may still describe a minor difference. Effect size gives more context. Cohen's d shows the difference in standard deviation units. Hedges' g adjusts d for smaller samples. Effect size r gives a correlation style measure. Eta squared estimates the share of explained variation.
Choosing the Right Design
The correct formula depends on the study design. Use the independent groups option for two separate groups. Enter both group sizes for that method. Use the paired or one sample option for repeated scores. That option also works for a one sample t test. Enter the total number of paired cases or observations.
Reading the Output
Cohen's d near 0.20 is often called small. A value near 0.50 is often medium. A value near 0.80 is often large. These labels are only rough guides. Your field may need different standards. Always compare the result with prior studies. Also consider measurement quality and sample design.
Confidence and Reporting
The confidence interval gives a useful range for d. A wide interval means the estimate is less precise. This can happen with small samples. A narrow interval usually means better precision. Report the t value, degrees of freedom, sample sizes, and effect size. Include the method used. This helps other readers verify the result.
FAQs
What is an effect size from a t test?
It is a practical measure of difference size. It helps explain how large the result is, not only whether the result is statistically significant.
Can I calculate Cohen's d from a t value?
Yes. For independent groups, use d = t × √(1/n1 + 1/n2). For paired or one sample tests, use d = t / √n.
What is Hedges' g?
Hedges' g is a corrected version of Cohen's d. It reduces small sample bias and is often preferred when sample sizes are limited.
What does effect size r mean?
Effect size r converts the t result into a correlation style value. It ranges from negative to positive and shows the strength of association.
Is eta squared the same as Cohen's d?
No. Eta squared estimates explained variation. Cohen's d describes mean difference in standard deviation units. Both summarize effect size differently.
Should I use one tailed or two tailed input?
The tail choice is stored for reporting context. The main effect size formulas use the t value, degrees of freedom, and sample sizes.
Why do I need sample sizes?
Sample sizes are needed to calculate Cohen's d and Hedges' g correctly. Effect size r and eta squared can use t and degrees of freedom.
Can I export my result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button to print or save a clean report from the browser.