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Analysis of Covariance: Johnson-Neyman Procedure

Steve M. Hunka
Organization: University of Alberta
Department: Professor Emeritus of Educational Psychology
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Analysis of covariance is used to assess the statistical significance of mean differences among experimental groups with an adjustment made for initial differences on one or more concomitant variables (covariates). The adjustment assumes that group regression coefficients are homogeneous, in which case the adjustment can be made to any value of the covariates. When coefficients are not homogeneous, the effect of the adjustment will be different for different values of the covariate to which groups are equated. The Johnson-Neyman procedure accommodates analyses when the regression coefficients are not homogeneous. The Mathematica program uses the general linear model approach using a mu-model design matrix, testing for homogeneity of regression, and through use of a symbolic contrast matrix calculates the polynomial representing the sum of squares for testing SS model corrected for the mean. The polynomial provides the basis for identifying boundaries of the covariates which result in statistically significant differences among the groups.

*Mathematics > Probability and Statistics

heterogeneous regression, general linear model
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*Analysis of Covariance: Johnson-Neyman Procedure; 3 Covariate Case   [in MathSource: Packages and Programs]
*Analysis of Variance   [in MathSource: Packages and Programs]
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ancovjn2.nb (525.9 KB) - Mathematica Notebook

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ancovjn2.ma (280.5 KB) - Mathematica Notebook