Consider a randomized controlled experiment with two treatment groups (A and B).

Question

Consider a randomized controlled experiment with two treatment groups (A and B). It is a fact that the observations within groups are not independent and the two group averages are not independent. (a). What is the basis for the lack of independence both within and between groups? (The answer is very short! I am not asking for a proof; rather, I am just asking for a reason.) (b). Despite the fact that there is lack of independence, the usual two-sample t-test (which assumes independence within and between groups), is still a valid test for the null hypothesis of equal means. Why?

Explanation / Answer

Question 4

Part a

The significant relationship or direct/indirect association or autocorrelation between and within groups is the basis for the lack of independence, because we know that due to association or autocorrelation observations within and between groups are related to each other.

Part b

Despite the fact that there is lack of independence, the usual two sample t test is not valid test for the null hypothesis of equal means because the assumption of independence between two groups is not satisfied. We only use the two sample t test if the two samples are independent of each other and if there are two dependent samples, then we use the paired t test for checking the difference between two means or equality of two means.

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