2.9 Summary

This chapter explained the basis for the hypothesis testing in frequentist statistics: the central limit theorem. This led to the t-test, specifically, the one-sample t-test (equivalent to the paired t-test) and the two-sample t-test (for unpaired data). The key summary statistics, the t-test and the p-value were discussed, along with the limitations of these statistics for arriving at conclusions about the existence/absence of an effect. Specifically, under low statistical power, Type M and S error have the consequence that neither significant nor non-significant results are interpretable. We learned how to compute statistical power using the power.t.test function and using simulation. Important applications of the t-test in factorial designs was discussed, along with the limitations imposed by the t-test; these limitations can lead to misleading conclusions. Finally, some common mistakes in the usage of t-tests were exemplified.