Independent Observations with Binary Dependent Variables

Abstract

We outline the application of STA to binary dependent variables using the STACMR software package. Binary variables consist of counts of “hits” (or “successes”) and “misses” (or “failures”) over a set of independent Bernoulli trials. In a given experimental design, it is supposed that such counts are obtained across a set of experimental conditions defined by the levels of one or more independent variables. Apart from the form of the data, the treatment of binary variables by STACMR differs from that of continuous variables in two ways: (1) The monotonic regression weights correspond to the number of trials in each condition rather than the precision of the means; and (2) because the distribution of counts is known to be binomial, the bootstrap resampling step is parametric (rather than distribution-free as in the case of continuous variables).