Examining the variations in the results of the Hotelling T test in case of changing baseline landmarks in the Bookstein coordinates.

Abstract

In many biological and biomedical investigations, the most effective way to analyze the forms of whole biological organs or organisms is by recording geometric locations of landmark points. If we want to compare shapes, then individuals should be translated, rotated and scaled in such a way that all of the individuals lie in a standard position and are centered. Bookstein conducted this process by choosing two landmarks as reference landmarks. Each individual is translated, rotated and scaled according to these reference landmarks. The aim of the present study is to examine the change in the p values in the case of choosing different baseline landmarks when performing the Hotelling T test, which is commonly used when comparing two sample shape configurations based on Bookstein coordinates. For this purpose, the changes in the p values were investigated in shape configurations that are composed of a different number of landmarks by taking all of the possible paired landmark combinations at different variance levels and sample sizes. As a result of the present study, it was observed that, with the increase in the landmark number, the number of possible baseline landmark combinations also increases and, for this reason, a substantial number of variations occur in the p values. Therefore, it is an important to decide which landmarks should be taken as reference landmarks when using the Bookstein coordinates.