The Two-Sample Dependent Tests are used to test if differences exist in means and dispersion of two dependent populations from which the samples were drawn. The sampling methods may be repeated measures or matched pairs.
Three tests are employed to compare dependent populations. The first is the One-Sample Test for Correlation, the second is the Matched-Pairs t-test for Variance, and the third is the Paired t-test for differences in the Mean.
The following hypotheses may be tested:
Where and are the population means from which the samples were drawn.
The first hypothesis set could also be written as:
Where is the average paired difference.
Where and are the population variances from which the samples were drawn.
Where t has n - 2 df
The p-value is flagged with an asterisk (*) when p <= alpha.