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ERIC Number: ED317598
Record Type: Non-Journal
Publication Date: 1990-Apr
Pages: 21
Abstractor: N/A
Reference Count: N/A
Fitting a Serial Correlation Pattern to Repeated Observations Lacking Sphericity.
Edwards, Lynne K.
One of the most frequently used research methods in education and psychology involves repeated observations on the same individuals. When sample sizes are relatively small and a multivariate analysis lacks power, there are currently two analytical options in testing time effects. One is to assume a time series structure to these observations, and another is to assume a conventional univariate mixed effect model without a time dependent structure. A restrictive assumption of error sphericity is required for both approaches. If sphericity is not satisfied, the test statistic from either approach is approximately distributed as the "F". The theoretical lowerbound for the sample estimate is shown to be larger when the covariance matrix has a particular type of stationary time series structure (i.e., a serial correlation pattern). A Monte Carlo study was conducted, which indicates that postulating a serial correlation pattern may not have practical advantages over not assuming such a correlational pattern, at least for small sample sizes. The likelihood ratio test for serial correlation frequently rejects the true null hypothesis. This tendency is most pronounced when sample sizes are small. When a serial correlation is high, up to 39% of the covariance matrices sampled from a population covariance matrix with a serial correlation pattern show equal or larger correction factors when such a pattern is not assumed. Six data tables are included. (Author/TJH)
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A