I need to understand in the above three t-tests which test where to use?
Hello Kusaraju,
1. The t-test for paired/correlated/dependent samples compares means of matched pairs of scores on some variable/measure. A common example might be if you measured performance on some task prior to training, and the same persons were again measured for task performance after training, the dependent t would be a plausible analytic tool (though you do have to make some assumptions about the nature of the scores).
2. Two-sample (independent) groups t-test would be applied to non-matched data. That is, you want to compare two (independent) batches of scores on some variable/measure. This requires assumptions of normality and homogeneity of variance (for model residuals). If the homogeneity assumption isn't viable, then you could use:
3. Two-sample (independent) groups t-test with separate variance estimates (instead of pooled variance estimate). Alternatively, other methods, such as Welch method, Brown-Forsythe method, or James' second order method could be applied (or other procedures, such as trimming or Winsorizing data before running the t-test could be applied).
Good luck sorting it out.
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