Data Spread: Standard Deviations, One Sample Z-Test, One Sample Binomial Test

Abstract

With continuous outcome data (Chap. 1), the standard deviation is generally used to estimate the spread in a data sample. The standard deviation is, then, used for multiple purposes like null-hypothesis testing and the computation of confidence intervals. With binary outcome data things are different. Instead of a mean value the number of responders is calculated as a “kind of” mean value. In a data sample with binary outcome (yes-no outcome), the spread is estimated with the equation, √(p(1−p), where p = the proportion of responders, otherwise called the (yes-data fraction versus all data). This chapter assesses how these estimators can be used in practice for testing null-hypotheses and confidence intervals of binary outcome data.