Spurious and non-spurious power in performance criteria for tests of discordancy

When evaluating the performance of discordancy tests both the type 11 error and the power function contain spurious and non-spurious elements as the test may not identify the contaminant observation. The probabilities that are associated with identifying as discordant a good observation and a contaminant observation are defined as spurious power and nonspurious power respectively. This nomenclature conveys the role of each as performance criteria for tests of discordancy. A general discussion of discordancy test performance criteria is presented, as is the case of tests for multiple outliers. Finally, the behaviours of the Grubbs single-outlier and multiple-outlier tests are studied using simulation.