Lecture K1 (2020-11-17): Variance Reduction Techniques, Part 1 - CRN's and Control Variates

This lecture primarily finishes the coverage of estimation of relative performance by walking through the three different 2-sample mean tests (paired-difference t test, pooled-variance t-test, and Welch's unpooled-variance t-test) and the assumptions required to use them. Confidence intervals for each of the mean differences are defined, requiring formulas for standard error of the mean and degrees of freedom for each of the three experimental cases. We also briefly discuss how to extend this to more than 2 systems (with ANOVA's and post-hoc tests), but due to time we shift into an introduction of the related topic of Variance Reduction Techniques (VRT's). We introduce common random numbers (CRN's), but the full discussion of CRN's and Control Variates will be saved until the next lecture.