Evaluating Spacing Tests of Multi-Modality

Abstract

The spacing of data contains information about the underlying modality. Sections of consistent, similar spacing correspond to modes while it increases between them. We have defined parametric, runs-based non-parametric, and data driven tests to evaluate these features --- flats and peaks --- and determine the presence and location of multiple modes. This report will check the tests in two situations. By varying a bi-modal setup we can control the changes in spacing and determine the resolution and sensitivity of the tests. By applying them to the large number of test cases that exist in the literature from other modality studies we check the stability and consistency of the results. We will also evaluate the accuracy of the null-distribution models of the features. The results show that the spacing does reflect the data's modality, that the tests do screen marginal cases, and where the analysis begins to break down.