I have a biological problem which involves using a 1-sided two-sample t-test. To simplify the problem, let’s assume an experiment comparing quantities in a control (C) and a treatment (T) group, each having 3 replicates, called C1, C2, C3, T1, T2, T3. Here, C1 and T1 are samples from the same subject, C2 and T2 are samples from the same subject, and so on.
Now I obtain a number for each of the following combinations. "within" = within group (i.e. both are C or both are T). Also, the number after C or T indicate whether they're from the same subject (sub) or not.
C1_C2 (within: different sub) C1_C3 (within: different sub) C1_T1 (between: same sub) C1_T2 (between: different sub) C1_T3 (between: different sub) C2_C3 (within: different sub) C2_T1 (between: different sub) C2_T2 (between: same sub) C2_T3 (between: different sub) … (a total of 15 pairwise quantities)
We are essentially interested in comparing the quantities "within" group and the quantities "between" group, but hoping to incorporating the "subject" effect somehow in the t-test. Is there a way to distinguish “different sub” and “same sub” in the test?
Thank you so much for your suggestions!!