Understanding Paired Two Tailed Testing
What It Compares
A paired two tailed t test compares two related measurements. The values may come from the same person, item, machine, class, or location. Each first value must match one second value. The test studies the list of differences, not the original columns alone.
When It Helps
This calculator is useful when you expect change, yet you do not know its direction. The result checks whether the average paired difference is meaningfully different from the hypothesized mean difference. Most users set that value to zero. A zero null value means the two paired conditions have no average change.
Main Statistic
The main statistic is the t value. It is found by dividing the adjusted mean difference by the standard error. The standard error is based on the sample standard deviation of the paired differences and the number of valid pairs. Larger absolute t values show stronger evidence against the null statement. The degrees of freedom equal the number of pairs minus one.
Two Tailed Evidence
A two tailed p value measures evidence in both directions. It counts results that are at least as extreme as the observed t value, whether positive or negative. When the p value is less than alpha, the calculator marks the result as significant. This does not prove importance. It only shows statistical evidence under the model.
Interval and Effect Size
The confidence interval adds practical meaning. It gives a likely range for the true mean paired difference. If the interval excludes the hypothesized value, it agrees with a significant two tailed test at the matching confidence level.
Effect size helps judge magnitude. Cohen dz uses the mean difference relative to the standard deviation of differences. The corrected value applies a small sample adjustment. These values are helpful when p values are affected by sample size.
Input Quality
Good input quality matters. Use matched rows. Keep units consistent. Do not sort one column without sorting the other. Remove pairs only when both related observations are not valid. For small samples, inspect the differences for extreme outliers. A paired t test is fairly robust, but severe outliers can distort the mean, standard deviation, and p value.
Reports
Use the exported reports to document work. The CSV file is useful for spreadsheets. The PDF file is useful for sharing a concise summary with others.