Appendix A - Statistics Background

Summary

In this appendix, we provide a brief review or introduction to some of the basic statistical concepts used in the chapters.

Statistical Significance

We will introduce the concept of statistical significance of treatment effects using the permutational approach. Suppose we have outcome data from n patients in a control group C and n patients in the experimental treatment group E. We want to test the null hypothesis that the experimental treatment is equivalent to the control in its effect on outcome. Let T denote a measure of difference between the outcomes on the experimental treatment and the outcomes on the control. With outcomes like blood pressure, we might define T as the mean outcome for patients on E minus the mean for those on C. With continuous outcome measures, the difference in mean outcomes is often standardized by the within-group standard deviation. If the outcome is a binary measure of response or no response, then T might be the difference between the treatment and control groups in the proportion responding.

If the null hypothesis were true, the outcomes would be the same whether patients were treated by E or C. This is called the global null hypothesis and is the one that we will consider. Let N denote the total number of patients. The N treatment assignments can be collected into a vector. The ith element of the vector is E if the ith patient to enter the clinical trial was assigned E; otherwise, the ith element is C.