So you want to test if the mean of a numeric outcome differs between two paired groups. Statistical tests on paired data actually convert each pair of values into a single measurement by taking the difference. For example, a subject’s pre-test score can be subtracted from their post-test score to get a change in score for each subject.
Question: Is the distribution of the differences normal?
A normal distribution is the classic bell curve. It is symmetric, with most cases falling near the mean and fewer cases falling away from the mean in either tail.
Example:
For more information: Assessing normality
If the variable’s distribution is skewed, has more than one mode (peak), or contains outliers, then it will fail the normality assumption of many parametric statistical methods.
Example:
