Assumptions underlying the t-tests and their extensions

The t-tests and their extensions ANOVA, ANCOVA and regression all make assumptions about the distribution of the data in the background populations. If these assumptions are not appropriate then strictly speaking the p-values coming out of those tests together with the associated confidence intervals are not valid. 

There is, in fact, one additional assumption that the above procedures make and that is independence the way a particular patient responds is not linked to the way another patient responds. In a randomised clinical trial this assumption is unlikely to be violated and we will not discuss this issue further here. 

Statistical Thinking for Non-Statisticians in Drug Regulation Richard Kay 2007 John Wiley Sons, Ltd ISBN 978-0-470-31971-0 

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