I am having a discussion with someone in Public Health / Program evaluation regarding the appropriateness of running an independent samples t test on data that is collected from the same participant at two different time points. They claim that within field Publich Health / Program evaluation an independent samples t can be and is appropriate for use. Thoughts?
If data are collected from the same subject at two different time points, the data are not independent of the other (i.e., the data are correlated, at least usually). A paired t-test (aka dependent samples t-test) is required to test for differences between the two time points. The choice of the appropriate statistical test has nothing to do with the research field. Furthermore, a paired t-test is more powerful than an independent samples t-test if run on the same data.
Indeed, paired data are not independent, irrespective of the research field. There is a lot of good literature on the underlying rationale and analysis approaches. There are a number of different approaches by which statistical comparisons may be conducted, depending on the nature of the data under consideration. Examples include paired samples t-test, Wicoxon, and linear mixed effects models where data pairs may be considered as a random effect.
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