<Li> The data used to carry out the test should be sampled independently from the two populations being compared . This is in general not testable from the data, but if the data are known to be dependently sampled (that is, if they were sampled in clusters), then the classical t - tests discussed here may give misleading results . </Li> <P> Most two - sample t - tests are robust to all but large deviations from the assumptions . </P> <P> Two - sample t - tests for a difference in mean involve independent samples or unpaired samples . Paired t - tests are a form of blocking, and have greater power than unpaired tests when the paired units are similar with respect to "noise factors" that are independent of membership in the two groups being compared . In a different context, paired t - tests can be used to reduce the effects of confounding factors in an observational study . </P> <P> The independent samples t - test is used when two separate sets of independent and identically distributed samples are obtained, one from each of the two populations being compared . For example, suppose we are evaluating the effect of a medical treatment, and we enroll 100 subjects into our study, then randomly assign 50 subjects to the treatment group and 50 subjects to the control group . In this case, we have two independent samples and would use the unpaired form of the t - test . The randomization is not essential here--if we contacted 100 people by phone and obtained each person's age and gender, and then used a two - sample t - test to see whether the mean ages differ by gender, this would also be an independent samples t - test, even though the data are observational . </P>

When do we use two sample t test
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