Compare paired observations with precise interval estimates and significance checks. Export results, inspect differences, and understand each calculation step clearly today.
| Pair | Before | After | Difference |
|---|---|---|---|
| 1 | 12 | 10 | 2 |
| 2 | 15 | 14 | 1 |
| 3 | 14 | 13 | 1 |
| 4 | 10 | 9 | 1 |
| 5 | 18 | 16 | 2 |
| 6 | 20 | 18 | 2 |
| 7 | 16 | 15 | 1 |
| 8 | 19 | 17 | 2 |
This example compares paired measurements from the same items before and after a change. Enter the same values into the form to test the calculator.
The paired t test confidence interval is based on the differences between matched observations. First compute each difference using di = xi - yi.
The mean difference is:
d̄ = (Σdi) / n
The sample standard deviation of differences is:
sd = √[Σ(di - d̄)² / (n - 1)]
The standard error is:
SE = sd / √n
The confidence interval for the true mean difference is:
d̄ ± tα/2, n-1 × SE
The t statistic for hypothesis testing is:
t = (d̄ - μd0) / SE
Here, μd0 is the hypothesized mean difference, often zero. Degrees of freedom equal n - 1 because the paired test uses the difference sample.
A paired t test confidence interval calculator helps estimate the average difference between two related measurements. It is useful when the same subjects, items, or units are measured twice. Common examples include before-and-after studies, repeated lab readings, training effects, and matched experimental conditions.
This calculator does more than produce one interval. It computes the paired differences, the mean of those differences, the sample standard deviation, the standard error, the t critical value, and the final confidence interval. It also reports the t statistic and p value for a hypothesis test, which makes the page useful for both classroom exercises and practical analysis tasks.
The most important rule is pairing. Each value in Sample 1 must match the same subject or unit in Sample 2. If the observations are independent rather than matched, a two-sample t procedure is more appropriate. The paired method reduces noise by focusing on within-pair change.
The graph adds another layer of understanding. When the plotted differences cluster above zero, the first condition tends to exceed the second. When they cluster below zero, the second condition tends to be larger. Wide spread in the differences usually leads to a larger standard error and a wider confidence interval.
The export features support reporting and documentation. Use CSV for spreadsheets and further analysis. Use PDF when sharing a clean summary with classmates, teachers, or colleagues. Because the calculator keeps the workflow in one page, it is convenient for quick checks, teaching demonstrations, and repeated statistical practice.
It estimates the mean difference between two related samples and builds a confidence interval around that mean difference. It also reports a paired t statistic and p value.
Use it when each observation in one sample directly matches one observation in the other sample. Examples include before-and-after measurements on the same subjects.
No. A paired analysis requires one matched value in Sample 1 for every matched value in Sample 2. Unequal counts break the pairing structure.
It gives a plausible range for the true population mean difference. If the interval excludes zero, that often suggests a meaningful difference between conditions.
The paired method studies within-pair change. That removes between-subject variation and often improves sensitivity when the same units are measured twice.
It lets you test claims about the average paired difference. The usual default is zero, but you may test another target value when needed.
Yes. The results section includes a pairwise table and a graph of all computed differences, which helps you inspect direction and spread.
Yes. You can download a CSV summary for spreadsheet work or create a PDF summary for records, assignments, or reporting.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.