#### Abstract

Many real data sets that would normally lend themselves to being analyzed by an analysis of covariance, have a covariate interaction present with one or more of the factors in the experiment. Because this violates the assumption of same-slope covariate effect across all treatments, an analysis of covariance should not be performed. The course normally taken when there is such an interaction is to derive regression equations for the dependent variable as a function of the covariate, at each level of the factor(s) being tested. A general linear model F-test can then be used to test whether there are any overall differences between the regression lines. A technique that uses two mathematical distance measures to detect regression line differences once a significant general linear model F-test is obtained is illustrated. Applying these distance measures enables us to perform modified multiple comparisons of the regressions without resorting to the use of multiple pairwise general linear model F-tests, which inflate the Type I error rate. with this method, we are able to incorporate both factor and covariate information into the analysis to overcome the covariate-factor interaction problem.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

Palmquist, D. E. and Stockwell, C. A.
(1995).
"COVARIANCE ANALYSIS WITH A COVARIATE INTERACTION: AN EXAMPLE OF A SIMPLE LINEAR REGRESSION COMPARISON TECHNIQUE,"
*Annual Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/1995/proceedings/3

COVARIANCE ANALYSIS WITH A COVARIATE INTERACTION: AN EXAMPLE OF A SIMPLE LINEAR REGRESSION COMPARISON TECHNIQUE

Many real data sets that would normally lend themselves to being analyzed by an analysis of covariance, have a covariate interaction present with one or more of the factors in the experiment. Because this violates the assumption of same-slope covariate effect across all treatments, an analysis of covariance should not be performed. The course normally taken when there is such an interaction is to derive regression equations for the dependent variable as a function of the covariate, at each level of the factor(s) being tested. A general linear model F-test can then be used to test whether there are any overall differences between the regression lines. A technique that uses two mathematical distance measures to detect regression line differences once a significant general linear model F-test is obtained is illustrated. Applying these distance measures enables us to perform modified multiple comparisons of the regressions without resorting to the use of multiple pairwise general linear model F-tests, which inflate the Type I error rate. with this method, we are able to incorporate both factor and covariate information into the analysis to overcome the covariate-factor interaction problem.