Repeated Measures T Test Calculator
Example Data Table
| Pair | Before Inspection | After Inspection | Difference |
|---|---|---|---|
| 1 | 10.2 | 10.8 | 0.6 |
| 2 | 9.8 | 10.1 | 0.3 |
| 3 | 10.5 | 10.9 | 0.4 |
| 4 | 10.1 | 10.4 | 0.3 |
| 5 | 9.9 | 10.0 | 0.1 |
| 6 | 10.3 | 10.7 | 0.4 |
| 7 | 10.0 | 10.2 | 0.2 |
| 8 | 10.4 | 10.9 | 0.5 |
Formula Used
The repeated measures t test compares paired observations from the same item, unit, or process across two conditions or times.
Difference for each pair: di = Afteri − Beforei
Mean difference: d̄ = Σdi / n
Standard deviation of differences: sd = √[Σ(di − d̄)² / (n − 1)]
Standard error: SE = sd / √n
T statistic: t = d̄ / SE
Degrees of freedom: df = n − 1
Confidence interval: d̄ ± tcritical × SE
This design reduces between-item variation because every measurement pair comes from the same source.
How to Use This Calculator
- Enter a dataset name for your quality study.
- Rename the two measure labels if needed.
- Set the alpha level for significance testing.
- Choose the alternative hypothesis direction.
- Paste one paired observation per line.
- Use commas or spaces between the two values.
- Click the calculate button.
- Review the t statistic, p value, interval, and effect size.
- Inspect the charts for pattern changes and spread.
- Export the results to CSV or PDF if needed.
FAQs
1. What does a repeated measures t test evaluate?
It tests whether the average difference between paired observations differs from zero. This is useful when the same process, product, or unit is measured twice under matched conditions.
2. When should I use this test in quality control?
Use it for before-after checks, calibration comparisons, operator interventions, machine adjustments, or process changes where the same units are measured twice.
3. What input format does the calculator accept?
Enter one pair per line. The first number is the first measure. The second number is the repeated measure. Use commas, spaces, tabs, semicolons, or pipes.
4. What does the p value tell me?
The p value estimates how likely your observed mean difference would appear if the true average change were zero. Smaller values indicate stronger evidence of a real shift.
5. Why is Cohen's dz included?
Cohen's dz measures effect size for paired data. It shows the magnitude of change relative to the spread of the differences, not just significance.
6. What assumptions matter most?
The differences should be roughly independent and approximately normal, especially for small samples. Large outliers in paired differences can distort the result.
7. Can I use this for unequal sample counts?
No. Each row must contain a complete pair. Repeated measures analysis requires matched values from the same unit, item, or process point.
8. What charts are displayed after calculation?
The page shows a paired line chart for both measures and a difference chart. These visuals help reveal direction, consistency, and unusual pair behavior.