Statistical Evaluation of Growth Curves

Abstract

In an article with the above title which appeared in this journal, 1 Weil compares the growth curves of groups of experimental animals subject to different treatments. Five treatments are compared against each other and a control, 30 rats are used for each treatment and the weight of each rat is determined at weekly intervals. Weil proposes a method of analysis in which he constructs a frequency distribution for each treatment taking all the weights of the rats over the period of the experiment and then applies the chi-square test to examine differences between those frequency distributions for the various treatments.

This is an oversimplified method of analysis and not a valid one. The fallacy lies in the tacit assumption that all the observations within each of the frequency distributions are independent. Although the 30 rats in each group are independent, the repeat weighings on each rat are certainly not so. In practically all biological work, the main source of variability lies between animals; repeat determinations per animal will result in more precise measurement for the individual animals, but will not reduce the effect of the basic variability between the animals. Applying the chi-square test in the way proposed by Weil may grossly overestimate the significance of the differences between the treatments.

There are valid methods of comparing growth curves of the type considered by Weil. These are indicated in broad outline in this note and a more detailed account with numerical examples will be published elsewhere.

In his paper, Weil considers the t-test applied to the weights after a given time, e.g. weights after 12 weeks. Provided the apportionment of the animals between the groups has been carried out in a strictly random manner, this method of test is valid.