摘要：The present article examines the behaviour of four univariate statistics for analyzing data in a mixed repeated measures design, the procedures of Greenhouse and Geisser (1959), of Lecoutre (1991), of Hearne, Clark and Hatch (1983) and of Jones (1985), which differ in how they approach the absence of sphericity, assuming either arbitrary correlation or serial autocorrelation. These four approaches were compared with respect to empirical power in conditions of multivariate normality and absence of normality, and of different underlying structures of covariance. Overall, when the distribution is normal, Monte Carlo comparisons indicate that when the matrix is stationary autoregressive or structured non-stationary autoregressive, the Lecoutre and Hearne et al. statistics are more powerful, the former enjoying slightly higher empirical power, with no large differences between the two in either direction of the autocorrelation (positive and negative first-order serial correlation). For an arbitrary non-stationary matrix, the Hearne et al. procedure is considerably more powerful than the Lecoutre statistic when the deviation of the sphericity is slight and severe, both in the two directions of the autocorrelation (positive and negative first-order serial correlation) and when it is arbitrary (correlation=0). When the data are underlain by a non-normal distribution, the HCH procedure is that with the greatest empirical power when the serial correlation is positive, and the JN procedure when the serial correlation is negative whatever the underlying deviation matrix.
关键词：Power of the test; stationary autoregressive matrix; structured non-stationary autoregressive matrix; arbitrary non-stationary autoregressive matrix; non-stationary matrix with arbitrary correlation.
