Cohen's d Paired t-test Calculator

Calculator Inputs

Example Data Table

Formula Used

Mean difference: d-bar = sum of paired differences / n

SD of differences: SDdiff = square root of sample variance of paired differences

Paired t value: t = (d-bar - hypothesized difference) / (SDdiff / square root of n)

Cohen's dz: dz = d-bar / SDdiff

Hedges correction: gz = dz × [1 - 3 / (4df - 1)]

Average SD version: dav = d-bar / average of the two condition standard deviations

Repeated measures version: drm = dz × square root of [2 × (1 - paired correlation)]

How to Use This Calculator

1. Select raw paired scores when you have both condition values.
2. Select summary statistics when you only know the mean difference, SD difference, and sample size.
3. Choose the difference direction carefully.
4. Enter a hypothesized mean difference, usually zero.
5. Press calculate to show results above the form.
6. Use CSV or PDF export for reports.

Understanding Paired Effect Size

A paired design measures the same subject twice. It may compare before and after scores. It may also compare two matched conditions. The paired t-test checks whether the average difference is large compared with difference variation. Cohen's d adds scale. It explains how large the change is in standard deviation units.

Why Paired Cohen's d Matters

A significant result can still be small. A non significant result can also hide a useful trend. Effect size helps readers judge practical value. In paired work, the key spread is often the standard deviation of the difference scores. That value includes the within person pattern. When scores move together, paired analysis usually gains precision.

Main Measures

This calculator reports Cohen's dz first. It divides the mean difference by the standard deviation of paired differences. It also reports Hedges corrected gz. That version reduces small sample bias. When raw data are entered, the tool can also show dav. It uses the average of the two condition standard deviations. The repeated measures adjusted value uses the paired correlation.

Interpreting Results

Common labels are only guides. Around 0.20 is often called small. Around 0.50 is often called medium. Around 0.80 is often called large. Your field may use different standards. Direction matters too. A positive value means the selected difference order increased. A negative value means it decreased.

Good Reporting Practice

Report the sample size, mean difference, standard deviation of differences, t value, degrees of freedom, p value, and effect size. Add the confidence interval when possible. Mention the direction used. For example, state that the difference was after minus before. This avoids confusion. With small samples, include Hedges correction. It gives a more conservative estimate.

Using Raw or Summary Data

Raw paired scores are best because the tool can verify pair counts and calculate correlation. Summary data are still useful for published results. Enter the mean difference, standard deviation of differences, and sample size. Use the same units throughout. Review warnings before using exports. The calculator supports quick reporting, but it does not replace study design, assumptions, or subject knowledge. Always keep raw records because transparent data make later checks easier for reviewers, teams, and future audits.

FAQs

1. What is Cohen's d for a paired t-test?

It is an effect size for repeated or matched data. The common paired version, dz, divides the mean paired difference by the standard deviation of paired differences.

2. Should I use raw scores or summary statistics?

Use raw scores when available. They let the calculator verify pair counts, calculate paired correlation, and produce more complete results. Summary inputs are useful for published data.

3. What does a positive dz mean?

A positive value means the chosen difference order is positive. If you choose Score B minus Score A, a positive dz means Score B is higher on average.

4. What is Hedges corrected gz?

Hedges corrected gz adjusts Cohen's dz for small sample bias. It is usually slightly smaller than dz, especially when the number of paired observations is low.

5. What is dav?

dav divides the mean paired difference by the average standard deviation of the two measurement conditions. It can help when comparing paired results with other standardized effects.

6. What is drm?

drm uses the paired correlation to adjust the repeated measures effect. It is shown when a valid correlation is available or calculated from raw paired scores.

7. Is the p value exact?

The calculator estimates the two-tailed p value from the t distribution. Results should be suitable for normal reporting, but specialist software may be preferred for regulated analysis.

8. Can I export the results?

Yes. Use the CSV button for spreadsheet data. Use the PDF button after calculation to save a simple report of the calculated values.