Maximising the power of comparing single cases against control samples: An argument, a program for making comparisons and a worked example from the Pyramids & Palm Trees test

In neuropsychological research, it is frequently necessary to compare the performance of a single case with that of a control sample. Recently, there has been a discussion about whether existing methods are adequate in preventing Type 1 errors due to increased variability in the single-case data (Crawford, Garthwaite, Howell, & Gray, 2004; Mitchell, Mycroft, & Kay, 2004; Mycroft, Mitchell, & Kay, 2002) and about the power of any comparisons. In this paper, we propose an extension of the modified t test introduced by Crawford and Howell (1998). We provide Monte Carlo simulations that show that it is possible to increase the power of the modified t test by retesting the single case. We also make available a computer program that implements the method introduced in this paper and that can be used by neuropsychologists to test for a difference between a single case and a control group. We apply our procedure to an example of a patient examined on the "Pyramids and Palm Trees" test.