t-test for paired samples

The paired t-test is a statistical test that determines whether the means of two sample sets differ significantly.

Given two paired sets X_i and Y_i of n measured values, the paired t-test determines whether they differ from each other in a significant way under the assumptions that the paired differences are independent and identically normally distributed. To apply the test, let X^^_i | = | (X_i - X^_) Y^^_i | = | (Y_i - Y^_), then define t by t = (X^_ - Y^_)sqrt((n(n - 1))/( sum_(i = 1)^n (X^^_i - Y^^_i)^2)).

Fisher sign test | hypothesis testing | Student's t-distribution | Wilcoxon signed rank test

college level (AP statistics)