Fitting a Serial Correlation Pattern to Repeated Observations

Abstract

When repeated observations are taken at equal time intervals, a simple form of a stationary time series structure may be fitted to the observations. Wallenstein and Fleiss (1979) have shown that the degrees-of-freedom correction factor for time effects has a higher lowerbound for data with a serial correlation pattern (or a simplex pattern) than for data without such a structure. The reanalysis of the example data found in Hearne, Clark, and Hatch (1983) indicated that the correction factor from a patterned matrix could be smaller than the counterpart without fitting a simplex pattern. First, an example from education was used to illustrate the computational steps in obtaining these two correction factors. Second, a simulation study was conducted to determine the conditions under which fitting a simplex pattern would be advantageous over not assuming such a pattern. Fitting a serial correlation pattern did not always produce more powerful tests of time effects than not assuming such a pattern. This was particularly true when correlations were high (ρ > .50). Furthermore, it inflated Type I error rates when the simplex shypothesis was not warranted. Indiscriminately fitting a serial correlation pattern should be discouraged.