Testing alternative methods of analysing differences in fish condition, with an example using the mosquitofish Gambusia holbrooki

Abstract

In this study we have examined two different methods, the ANCOVA and a weighted procedure, in order to highlight the problems associated with the use of ANCOVA when the assumption of homogeneity of error variances among data sets is wrongly assumed. When error variances are unequal, ANCOVA procedure may lead to estimates of common regression coefficients with larger standard error values than those obtained when a weighted method is employed. Moreover, the ANCOVA test for homogeneity of regression coefficients seems to be differently affected when error variances are not all equal. Specifically, in the case of unequal sample sizes, when large error variance is combined with the small group and the larger: smaller error variance ratio was more than 2, ANCOVA tests for homogeneity of regression coefficients could be substantially affected leading to a Type I error. Although the ANCOVA approach is a simple and robust method in testing for equality of regression coefficients and related analysis, its application should be preceded by tests to determine homogeneity of error variances to ensure its correct use and avoid erroneous interpretations of the data analysed. The weighted method could be considered as a valuable alternative method to ANCOVA when homogeneity of error variances and regression coefficients cannot be assumed. Data for Gambusia holbrooki from Lake Banyoles and Alt Emporda salt marshes (Catalonia, Spain) are used to illustrate these procedures.