How Percentage Yields and Other Scaled Data Should Be Analyzed and Presented

Animal Scientists are often interested in finding proportions, or percentages, in their response criteria (% yield, % bone ash, etc.). Whenever two normally distributed variables are “scaled”, dividing one normally distributed variable (the numerator) by another (the denominator), the result has a Cauchy, i.e, non-normal distribution. If there is little variation in the denominator, there is little skewing of the distribution from normal. As the variation in the denominator increases, skewing of the distribution increases. Experimental results can show significant differences in treatment effects on either/or the numerator and denominator, but no significant differences in their ratio. If only observing effects on a ratio, or proportion, it is not possible to observe an interaction between the treatment and denominator. When an Analysis of Variance (ANOVA) is conducted for a response variable, the probabilities of the treatment and scaling response variable (denominator) can be calculated. If there is an interaction between the treatment and another response variable, then both should be identified as contributing factors to the response variable (numerator). Any ratios or proportions that are calculated for purposes other than hypothesis testing should be qualified. Proportions and percentages are only appropriate when the levels of the interacting variables are specified.