N = 1 Designs: The Failure of ANOVA-Based Tests

Abstract

Several methods have been proposed for the analysis of data from single-subject research settings. This research focuses on the modifications of ANOVA-based tests proposed by Shine and Bower, a procedure that precedes the ANOVAF test by preliminary testing of within-phase lag one serial correlation and the one-way ANOVA as presented by Gentile, Roden and Klein. Monte Carlo simulation is used to investigate these tests with respect to robustness and power. Each test was analyzed under various patterns of serial correlation, various patterns of phase and trial means, normal and exponential distributions, and equal and unequal phase variances. The findings indicate that the probability of a Type I error for these ANOVA-based tests is seriously inflated by nonzero serial correlation. These tests, therefore, cannot be recommended for use with data that have nonzero serial correlation.