Calculator
Example Data Table
| Pair | Before | After | After minus before |
|---|---|---|---|
| 1 | 72 | 75 | 3 |
| 2 | 68 | 70 | 2 |
| 3 | 75 | 78 | 3 |
| 4 | 71 | 74 | 3 |
| 5 | 69 | 72 | 3 |
Formula Used
The calculator first creates paired differences using the selected direction.
d = second value - first value, or d = first value - second value.
Mean difference: d̄ = Σd / n
Sample standard deviation: sd = √[Σ(d - d̄)² / (n - 1)]
Standard error: SE = sd / √n
Test statistic: t = (d̄ - μ0) / SE
Degrees of freedom: df = n - 1
Confidence interval: d̄ ± tcritical × SE
How to Use This Calculator
- Enter labels for both paired samples.
- Paste matching values into both value boxes.
- Keep every row paired with the same subject or item.
- Select the difference direction used in your study.
- Enter the hypothesized mean difference, usually zero.
- Choose the tail type, alpha, and confidence level.
- Press Calculate to view the result above the form.
- Use CSV or PDF buttons to export the report.
Understanding Paired T Testing
A paired t test checks whether the average difference between two matched measurements is meaningfully different from a chosen value. The same subject, item, class, patient, batch, or account appears twice. That pairing removes much outside variation. It also makes the test stronger than a regular two sample test when pairing is real.
When The Test Fits
Use this method for before and after studies. Use it for matched designs. Use it for repeated measurements on the same unit. Common examples include weight before a plan, scores before training, machine output before repair, or blood pressure before treatment. Each first value must match the second value in the same row.
What The Calculator Does
The calculator subtracts each pair and studies those differences. It finds the mean difference, sample standard deviation, standard error, degrees of freedom, t statistic, p value, and confidence interval. It also reports Cohen's dz, Hedges adjusted effect, and an effect correlation. These values help explain both statistical evidence and practical size.
Why Tail Choice Matters
A two tailed test checks for any change. A right tailed test checks whether the mean difference is greater than the hypothesized value. A left tailed test checks whether it is smaller. Pick the direction before reviewing the result. Changing tails after seeing data can make the conclusion misleading.
Reading The Result
The t statistic compares the observed mean difference with the expected difference. A larger absolute value shows stronger evidence against the null claim. The p value gives the probability of seeing evidence this extreme when the null claim is true. If the p value is below alpha, the calculator marks the result as significant.
Good Data Practice
Enter clean matched data. Remove empty rows. Keep units consistent. Do not mix percentages with raw numbers. Review outliers before deciding. A paired t test assumes the differences are roughly normal, especially for small samples. With larger samples, the method is more tolerant. Still, a plot or summary of differences is useful. Export the report when you need a record for audits, homework, lab notes, or business reviews. Always keep original paired records available. They help reviewers later confirm matching, units, assumptions, and any unusual observations clearly too.
FAQs
What is a paired t test?
It is a test for two related measurements. Each first value must match one second value. The test checks whether the mean paired difference differs from a hypothesized value.
When should I use this calculator?
Use it for before and after studies, repeated measurements, matched subjects, or paired items. Do not use it for two unrelated groups.
What is the t statistic?
The t statistic measures how far the observed mean difference is from the hypothesized difference. It uses the standard error as the scale.
What does the p value mean?
The p value shows how unusual the observed evidence is under the null hypothesis. A smaller value gives stronger evidence against the null claim.
What is the usual alpha value?
Many studies use 0.05. Some use 0.01 or 0.10. Choose alpha before viewing the result.
What is Cohen dz?
Cohen dz is an effect size for paired data. It divides the mean difference by the sample standard deviation of the differences.
Can paired values be negative?
Yes. The original values and differences may be negative. The calculation still works if each pair is correctly matched.
Why must sample sizes match?
A paired test compares values row by row. Each first value needs one related second value. Unequal counts break the matched design.