Formula Used
Mean difference: D bar = sum of paired differences / n.
Paired t value: t = D bar / (SD of differences / square root of n).
Cohen dz: dz = D bar / SD of differences.
Hedges corrected dz: gz = dz × J, where J = 1 - 3 / (4df - 1).
Average standardized difference: dav = D bar / square root of ((SD1 squared + SD2 squared) / 2).
Repeated measure adjusted value: drm = dz × square root of 2 × (1 - r).
Approximate interval: dz plus or minus z × standard error of dz.
How to Use This Calculator
Select raw score mode when you have each paired observation. Enter first condition values in the first box. Enter matching second condition values in the second box. Keep pairs in the same order.
Select summary mode when you only have sample statistics. Enter n, mean difference, and SD of differences. You may also enter condition means, condition SD values, and correlation for extra effect size options.
Choose the difference direction before calculation. Press calculate to show results below the header and above the form. Use the CSV or PDF buttons to export the same report.
Example Data Table
| Pair |
First condition |
Second condition |
Difference |
| 1 | 64 | 70 | 6 |
| 2 | 70 | 74 | 4 |
| 3 | 68 | 72 | 4 |
| 4 | 75 | 80 | 5 |
| 5 | 72 | 75 | 3 |
Understanding Paired Effect Size
A paired samples t test studies two linked measurements. The same person, item, or unit is measured twice. The test shows whether the average change is different from zero. Effect size shows how large that change is. It adds meaning beyond a p value.
Why This Calculator Helps
Repeated measure designs often use small samples. A significant result may still be small in practice. A non significant result may still be useful. This calculator reports several paired effect sizes. You can enter raw paired scores or summary statistics. It then calculates the mean difference, standard deviation of differences, standard error, t value, degrees of freedom, and approximate p value.
Important Effect Size Choices
Cohen's dz divides the mean difference by the standard deviation of paired differences. It is closely tied to the paired t statistic. Hedges corrected dz adjusts the value for small sample bias. Average standardized difference divides the mean change by the average standard deviation of the two conditions. This can be easier to compare with independent group studies. The repeated measure adjusted value uses the pre post correlation to describe change with dependence considered.
Reading The Results
The sign of the effect depends on the selected direction. A positive value usually means the second condition is higher. A negative value means the second condition is lower. Always define the direction before reporting results. Magnitude rules are only rough guides. Values near 0.20 are often called small. Values near 0.50 are often called medium. Values near 0.80 are often called large. Context matters more than labels.
Best Practice
Use raw paired scores when possible. Raw data gives better checks for missing pairs and variation. Summary inputs are helpful when you only have published statistics. Report the sample size, mean difference, standard deviation of differences, effect size type, confidence interval, and direction. Mention whether the value was bias corrected. Also report the paired t test result when it is relevant. Clear reporting helps readers understand both statistical evidence and practical importance.
Common Mistakes
Do not mix unpaired formulas with paired data. Do not ignore correlation. Check outliers, reversed scores, and units before interpreting the final estimate with care, context, and clear notes.
FAQs
What is paired samples effect size?
It measures the size of change between two linked measurements. The same subject, unit, or item appears in both conditions.
Which effect size is most common here?
Cohen dz is common for paired t tests. It divides the mean paired difference by the standard deviation of paired differences.
Why is direction important?
The sign depends on subtraction order. Second minus first gives a positive value when the second condition is higher.
Can I use only summary statistics?
Yes. Enter sample size, mean difference, and SD of differences. Add condition SD values and correlation for more outputs.
What does Hedges correction do?
It reduces small sample bias. This is useful when the paired sample size is limited.
What is dav?
dav standardizes the mean change by the average condition standard deviation. It helps compare paired results with other study designs.
Is the p value exact?
The calculator uses a t distribution approximation. It is suitable for normal paired differences and general reporting checks.
Should I report all effect sizes?
No. Choose the effect size that matches your research question. Report the formula, direction, sample size, and confidence interval.