Compative robustness of six tests in repeated measures designs with specified departures from sphericity

Compative robustness of six tests in repeated measures designs with specified departures from... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

Compative robustness of six tests in repeated measures designs with specified departures from sphericity

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media B.V.
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-008-9198-3
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Quality & QuantitySpringer Journals

Published: Sep 13, 2008

References

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