Calculator
Formula Used
Mean difference: d̄ = mean(after - before), or the selected reverse direction.
Paired t value: t = d̄ / (SDdiff / √n)
Cohen dz: dz = d̄ / SDdiff
Cohen dav: dav = d̄ / ((SDbefore + SDafter) / 2)
Cohen drm: drm = dz × √(2 × (1 - r))
Hedges correction: g = d × [1 - 3 / (4df - 1)]
Difference SD from summaries: SDdiff = √(SDbefore² + SDafter² - 2r × SDbefore × SDafter)
How to Use This Calculator
Select raw data when you have paired observations. Enter before values and after values in the same order. Use commas, spaces, semicolons, or new lines.
Select summary statistics when you only know means, standard deviations, sample size, and paired correlation. Enter SD of differences if it is already available.
Choose the difference direction. Then select alpha for confidence intervals. Press Calculate. Use CSV or PDF buttons to save the result.
Example Data Table
| Subject | Before | After | After - Before |
|---|---|---|---|
| 1 | 12 | 15 | 3 |
| 2 | 14 | 16 | 2 |
| 3 | 13 | 15 | 2 |
| 4 | 16 | 19 | 3 |
| 5 | 15 | 18 | 3 |
| 6 | 18 | 21 | 3 |
Understanding Paired Effect Size
A paired t test checks change within the same subjects. The test gives a p value. Effect size adds practical meaning. It tells how large the change is, not only whether it is detectable. This calculator reports paired measures.
Why Paired Designs Need Care
Repeated scores are linked. A before score and an after score come from the same person, unit, batch, or specimen. That link reduces random noise. It changes the standardizer used in the effect size. An independent groups formula can overstate or understate the paired effect. Correlation between paired scores matters, especially when summary values are entered.
Main Measures Reported
Cohen dz divides the mean difference by the standard deviation of the differences. It is common for power analysis and repeated measurement studies. Cohen dav divides the mean difference by the average of the condition standard deviations. It is easier to compare with independent group effects. Cohen drm adjusts dz with the paired correlation. It helps describe repeated measures while considering dependence. Hedges corrections reduce small sample bias.
Interpreting Results
A positive value means the after score is greater, based on the selected direction. A negative value means the after score is lower. Common labels are small, medium, and large. They are only rough guides. Field standards matter more. Medical, education, chemistry, and psychology studies may treat the same value differently.
Confidence Intervals
The interval shows a likely range for the true effect. A narrow interval means better precision. A wide interval means uncertainty remains. Small samples often create wide intervals. Outliers can also stretch the interval. Always inspect differences before trusting the number.
Practical Reporting Tips
Report the sample size, mean difference, standard deviation of differences, t value, degrees of freedom, p value, selected effect size, and confidence interval. Mention whether raw data or summary data were used. Keep the direction clear. State which condition was subtracted. Export the table when you need a record for a lab report, thesis, or audit.
Good Data Habits
Enter matched pairs in the same order. Remove empty rows. Do not mix subjects. Use consistent units. Review warnings before copying results. The calculator supports quick checks, but final research should use clean data and documented methods.
FAQs
What is paired t test effect size?
It measures the size of change between two related measurements. It adds practical meaning to the paired t test result.
When should I use Cohen dz?
Use Cohen dz when the standard deviation of paired differences is the best standardizer. It is common for repeated measures.
What is Cohen dav?
Cohen dav divides the mean difference by the average of the two condition standard deviations. It is useful for comparison.
Why is paired correlation important?
Paired correlation shows how strongly repeated scores move together. It helps compute SD of differences from summary statistics.
Can I enter raw paired data?
Yes. Enter before and after values in matching order. The calculator will compute differences, correlation, and effect sizes.
Can I use summary statistics only?
Yes. Enter sample size, means, standard deviations, and paired correlation. Add SD of differences if you know it.
What does a negative effect size mean?
It means the change is in the opposite direction of your selected subtraction rule. Check the chosen direction before reporting.
Are the confidence intervals exact?
The effect size intervals are approximate. They are useful for quick reporting, but advanced research may require specialized software.