Calculator Input
Example Data Table
| Subject | Control | Treatment A | Treatment B |
|---|---|---|---|
| 1 | 12 | 16 | 13 |
| 2 | 14 | 18 | 15 |
| 3 | 13 | 17 | 14 |
| 4 | 15 | 19 | 16 |
| 5 | 16 | 20 | 15 |
Formula Used
Paired t test
d = x1 - x2
t = mean(d) / (sd(d) / sqrt(n))
df = n - 1
Welch two sample t test
t = (mean1 - mean2) / sqrt((s1² / n1) + (s2² / n2))
df = ((s1² / n1 + s2² / n2)²) / (((s1² / n1)² / (n1 - 1)) + ((s2² / n2)² / (n2 - 1)))
Pooled two sample t test
sp² = (((n1 - 1)s1²) + ((n2 - 1)s2²)) / (n1 + n2 - 2)
t = (mean1 - mean2) / sqrt(sp²(1 / n1 + 1 / n2))
df = n1 + n2 - 2
Multiple comparison adjustments
Bonferroni adjusted p = min(p × m, 1)
Holm adjustment sorts p values from smallest to largest.
How to Use This Calculator
- Enter each group on a new line.
- Use a colon after the group name.
- Separate values with commas, spaces, or semicolons.
- Select paired, Welch, or pooled testing.
- Choose the alternative hypothesis.
- Select a p value adjustment method.
- Set confidence level, alpha, and decimal places.
- Press Calculate, CSV, or PDF.
Pairwise T Test Calculator Guide
A pairwise t test compares several group means in pairs. It is useful after a study has more than two samples. The calculator runs every possible comparison. It reports the mean difference, t statistic, degrees of freedom, p value, adjusted p value, confidence interval, and effect size.
Why Pairwise Testing Matters
A single t test answers one narrow question. Many research projects need more detail. You may compare a control group with many treatments. You may compare before and after scores across repeated conditions. Pairwise testing shows which exact groups differ. It also keeps the work organized in one table.
Available Test Choices
The paired option is best when values belong together. Use it for pretest and posttest data, matched subjects, or repeated measurements. The Welch option is useful when groups are independent and variances may differ. The pooled option assumes equal variances. It is suitable only when that assumption is reasonable.
Multiple Comparison Control
Running many tests increases the chance of false positives. This calculator includes Bonferroni and Holm adjustments. Bonferroni is simple and conservative. Holm is often less conservative while still controlling family wise error. You can also select no adjustment when exploratory results are acceptable.
Reading the Output
The p value shows evidence against the null hypothesis. The adjusted p value is better for final decisions when many pairs are tested. The confidence interval shows a practical range for the mean difference. The effect size shows the difference in standard deviation units. This helps judge importance, not only significance.
Good Data Practice
Enter clean numeric data. Check outliers before trusting results. Keep paired groups in the same order. Do not mix matched and independent designs. Review assumptions before reporting. Statistical software helps compute results, but sound study design still matters most.
When Results Are Strongest
Results are strongest when sample collection is planned before analysis. Balanced groups help precision. Larger samples reduce uncertainty. Clear labels prevent mistakes during export. Save the CSV for spreadsheets. Save the PDF for a quick report. Always describe the test choice, adjustment method, confidence level, and alpha value with the result. This makes later review easier for teams, instructors, reviewers, and clients before final publication and sharing.
FAQs
What is a pairwise t test?
It is a set of t tests. Each test compares one group with another group. The calculator runs all possible pairs from the groups you enter.
When should I use a paired t test?
Use it when observations are matched. Common examples include before and after scores, repeated measures, twins, or matched subjects.
When should I use Welch testing?
Use Welch testing for independent groups when variances may not be equal. It is often safer than assuming equal variances.
When should I use pooled testing?
Use pooled testing only when independent groups have similar variances. It assumes equal population variances across the compared groups.
Why adjust p values?
Many pairwise tests increase false positive risk. Adjustments reduce that risk and make the final comparison table more reliable.
What does adjusted p mean?
It is the p value after correcting for multiple tests. Use it for significance decisions when many pairs are compared.
What is effect size?
Effect size expresses the mean difference in standard deviation units. It helps judge practical importance beyond the p value.
Can I export the results?
Yes. Use the CSV button for spreadsheet work. Use the PDF button for a simple report file.