Influence Functions for Testing

Influence functions for testing are defined by applying Hampel's influence function to transformed P values. These influence functions describe the effect of an observation and an underlying distribution on the behavior of a test. Because these influence functions are not based on the test statistic alone, they are applicable to both unconditional and conditional (e.g., randomization) tests. The influence function of a transformed P value at a null hypothesis distribution is related to an influence function based on limiting power. The influence functions of several one- and two-sample tests for location are discussed to illustrate the utility of this approach.