To perform this test, select
.For example, suppose managers at a fitness facility want to determine whether their weight-loss program is effective. Because the "before" and "after" samples measure the same subjects, a paired t-test is the most appropriate analysis.
The paired t-test calculates the difference within each before-and-after pair of measurements, determines the mean of these changes, and reports whether this mean of the differences is statistically significant.
A paired t-test can be more powerful than a 2-sample t-test because the latter includes additional variation occurring from the independence of the observations. A paired t-test is not subject to this variation because the paired observations are dependent. Also, a paired t-test does not require both samples to have equal variance. Therefore, if you can logically address your research question with a paired design, it may be advantageous to do so, in conjunction with a paired t-test, to get more statistical power.
The paired t-test also works well when the assumption of normality is violated, but only if the underlying distribution is symmetric, unimodal, and continuous. If the values are highly skewed, it might be appropriate to use a nonparametric procedure, such as a 1-sample sign test.
H_{0}: μ_{d} = μ_{0} | The population mean of the differences (μ_{d}) equals the hypothesized mean of the differences (μ_{0}). |
H_{1}: μ_{d} ≠ μ_{0} | The population mean of the differences (μ_{d}) does not equal the hypothesized mean of the differences (μ_{0}). |
H_{1}: μ_{d} > μ_{0} | The population mean of the differences (μ_{d}) is greater than the hypothesized mean of the differences (μ_{0}). |
H_{1}: μ_{d} < μ_{0} | The population mean of the differences (μ_{d}) is less than the hypothesized mean of the differences (μ_{0}). |