A searching procedure for transformations and models in a classical Mendelian cross breeding study

Adopting Wright's four criteria (homogeneity, normality, additivity of effects, and parsimony of parameters needed) concerning a good scale of measurement, a systematic procedure is presented to find an adequate transformation for the data of a classical Mendelian cross. By using Cavalli's least-squares fitting procedure, fits of all possible genetical (sub)models are compared to each other. The model yielding the best fit with as few parameters as possible is selected. More complex models are accepted only if they fit significantly better than simpler ones. Four worked examples are presented from a classical cross study in rats: time till onset of a learned bar-press response under a continuous-reinforcement schedule and protein content, acetylcholinesterase activity, and butyrylcholinesterase activity in the occipital cortex. Using several transformations, invariance of resulting models was found if the criterion of homogeneity of variance was met.