In this article we examine the behaviour of six univariate statistics for analyzing the data of a Split-plot factorial design. Except for the univariate analysis of variance, which assumes that the dispersion matrix underlying the data is spherical, the other five procedures assume absence of sphericity. However, they do so with a clear distinction between two alternatives, insofar as three of them presuppose an arbitrary correlation between the data and two presuppose serial autocorrelation. These six approaches were compared with regard to their robustness under multivariate normality in the absence of sphericity, both when there was serial autocorrelation and when there was underlying arbitrary correlation. In general, Monte Carlo comparisons show that when underlying the data there is a autoregressive stationary or decreasing structured non-stationary autoregressive process, the Hearne, Clark and Hatch procedure is the most robust. In the rest of the conditions studied, i.e., increasing structured non-stationarity autoregressive and arbitrary non-stationarity (autoregressive and with arbitrary correlation), the Greenhouse-Geisser and Lecoutre statistics display the best behaviour.
Quality & Quantity – Springer Journals
Published: Sep 13, 2008
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