STATISTICAL APPROACH FOR ANALYZING CHANGES OVER TIME IN
OUTCOMES OF INTEREST
This appendix describes the statistical approach we used to estimate changes over time in the outcomes of interest. To illustrate the approach, we report results for the proportion of challenged evidence in which reliability was addressed, the proportion of challenged evidence found unreliable given that reliability was addressed (the success rate for reliability challenges), and the proportion of challenged evidence found unreliable. Similar estimates were made for the other outcomes of interest.
We modeled the outcomes of interest using a logistic model. The model includes case type, substantive area of challenged evidence, appellate circuit in which district court lies, and time period in which opinion was issued. Each characteristic (case type, substantive area of evidence, appellate circuit time period) is broken down into several categories, and one category is chosen as the reference category for each characteristic.
In the logistic model, the outcome is a Bernoulli random variable taking on the values of 0 or 1. The expected value of the outcome, E(Yi) = πi, is the probability that the outcome for the ith observation takes the value 1 and is a function of several explanatory variables: