Dealing with heterogeneous regression slopes in analysis of covariance: new methodology applied to environmental effects monitoring fish survey data

Analysis of covariance (ANCOVA) is a powerful statistical method which incorporates one or more covariates into the analysis to reduce error associated with measurement. ANCOVA (modeling response as a function of fish size) is frequently used to analyze environmental effects monitoring (EEM) fish survey data. In approximately 12% of fish survey data sets taken from cycles 1 to 3 of Environment Canada's EEM database for pulp and paper mills, the standard assumption of parallel regression slopes is not met. For the first three cycles of the EEM program, these data sets were classified as indicating a mill effect, but for the most part were excluded from subsequent analyses aimed at quantifying the effect. We present two different methods for initially dealing with data sets that exhibit heterogeneous slopes so that they can be analyzed using the parallel slope model. The first method identifies data sets where heterogeneous slopes are forced by a few high-influence observations. The second approach identifies data sets where a model with heterogeneous slopes is statistically, but not practically, significant: with a high coefficient of determination for the parallel slope model. These new methodologies are applied to EEM pulp and paper data sets and about 55% of cases with heterogeneous slopes can be described by a parallel slope model. We also discuss a third method that can be used to describe mill effects when regression slopes remain heterogeneous even after applying the above two methods, enabling comparison with a critical effect size. These new methodologies could benefit the EEM program by enabling more data sets to be incorporated into meta-analyses and be used to make more equitable mill monitoring decisions in the future.