Inference about means for matched pair design . Z-distribution with mean . t-distribution with mean . For comparing two treatments, the two basic types of design are: independent samples, 1 = 2 = use t-test with pooling. 1 (cid:54)= 2 = use t-test without pooling: matched pairs. Independent two-sample: one subject in one sample does not correspond to another subject to another sample. Dependent two-sample: one subject in one sample corresponds directly to another subject in another sample. Dependent samples of matched pair design use di erent treatments on the same subjects of a sample. Inference about 1 2 for two independent samples: we consider following two cases: case 1: 1 = 2 = is unknown, case 2: 1 and 2 are unknown and unequal. Case 1 (unknown population standard deviations are equal): suppose that the two normal population distributions have same standard deviation. Call the common-and still unknown-standard deviation of both populations .