Difficulties of Interpreting Multi-Slope Analysis of Covariance from Statistical Computer Packages

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Abstract
Many statistical computing packages can be used to obtain analyses of covariance fitting different regression slopes for each group. The output from most packages easily can be misinterpreted. Least squares means, differences among them, and analysis of covariance vary according to the reference point for the covariate. Because the analysis of covariance and least squares means provided by many packages are based on different reference points, namely, the intercept and the overall mean of the covariate, respectively, the 2 sets of statistics need not correspond. Significance tests for group differences based on them may suggest contradictory conclusions. These 2 reference points may be of little interest in a specific application. In some packages such as LSML76, the user can specify the reference points directly. In others, it is possible by a shift in the covariate to obtain the analysis of covariance for any reference point directly and least squares means with simple calculations. Some computer packages require the user to generate extra covariates when fitting the different slope model, a procedure that leads to incorrect least squares means. When the regression slopes vary, the researcher generally should avoid drawing an inference based on an arbitrary reference point but instead refer to the regression point but instead refer to the regression lines as a whole. Where a specific point is of interest, care should be taken that both analysis of covariance and least squares means related to this point.