On the effect of using ratios in the analysis of variance

Comparative virulence of Beauveria bassiana isolates against lepidopteran pests of vegetable crops

“…The potential for significant non-normality of ratio data must be taken into consideration in any application of parametric ANOVA. In a simulation study, Anderson and Lydic (1977) observed that the power of an ANOVA of ratios was highly dependent upon the ratio of the CVs of the numerator and denominator variables and concluded that ANOVA of ratios was acceptable under the condition that the CV of the denominator was 6 the CV of the numerator. The results from our study support this observation.…”

“…Assays were blocked over time; block interactions were not tested due to potential restriction error (Sokal and Rohlf, 1995). LC 50 values are derived as the ratios of the variables from the linear equations of log dose-probit mortality lines (intercept/ slope), and ratio data are generally not normally distributed (Anderson and Lydic, 1977;Sokal and Rohlf, 1995). The large numbers of screening assays of the selected standard strain (GHA) conducted against five host species provided an unique opportunity for detailed investigation of the nature of the distributions of the variables obtained from the probit regressions.…”

Correlates of sexual dimorphism in primates: Ecological and size variables

“…However, since the effects of weight are removed from dimorphism by taking a ratio only when the regression slope of male with female weight is 1.0 (Huxley, 1932), this measure is inappropriate for the study of weight's effects on weight dimorphism. Also, ratios of normally distributed variables are typically skewed to the right and leptokurtotic, making their use in regression and analysis of variance questionable (Atchley et al, 1976;Anderson and Lydic, 1977). The use of the difference between male and female means as a measure of dimorphism also allows an easier integration of between-species analyses with evolutionary theory and laboratory experiments in the evolution of sex dimorphism (Bird and Schaffer, 1972;Eisen and Hanrahan, 1972).…”

The Length and Proportions of the Thoracolumbar Spine in Children with Idiopathic Scoliosis

“…The two-tailed test was used in all cases. Since the statistical treatment of ratios may produce misleading results (Anderson & Lydic 1977) it was decided against performing any such procedures in the present study.…”