In this lecture, we review the fundamental tradeoffs in hypothesis testing and the concrete origins of the assumptions in both the t-test and Chi-square test. We also discuss parametric and non-parametric statistics (including exact and non-exact tests) and how non-parametric, exact statistics like the Kolmogorov–Smirnov test are derived. This culminates in a discussion of the multiple comparisons (MC) problem and the Bonferroni correction as well as alternative tests (such as a MANOVA or an ANOVA with post hoc test) that have more statistical power than the Bonferroni correction. We close with an introduction to performance inference from simulation, which we will continue discussing in the next 3 lectures.
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