The AstroStat Slog

From arxiv/astro-ph:0709.1073v1
On the Metallicity-Color Relations and Bimodal Color Distributions in Extragalactic Globular Cluster Systems by M. Cantiello and J. P. Blakeslee

Many observations on globular cluster systems (GCS) show bimodal distributions in color and metallicity space. The authors discussed the complication of non-linear metalicity and color relations and presented their careful study to suggest the optimal color(s) for revealing the presence of real bimodal GC metallicity distributions. Based on their simulation study, (V-H) and (V-K) are confirmed to be good colors for revealing unbiased bimodal metallicity distributions in GCS.

Asides, I’d like to comment on KMM code, which paper mentioned for testing bimodality.
Few years ago, I’ve noticed some papers that misinterpreted/misused this KMM method to test multi-modality of globular clusters in color space without knowing what is the objective, or the null hypothesis of the KMM method, which is, to my understanding, H_o: p=0, meaning that the second component contribution is none. The KMM test is a likelihood ratio test for H_o: one component vs H_1: two components; therefore, computing this KMM for testing one component vs three or two components vs three certainly introduces bias in estimating test statistics so that the resulting number cannot be compared with p-values from the asymptotic distribution of the KMM for testing hypotheses.

The KMM method is astronomers’ jargon to specify a likelihood ratio test for testing one normal distribution vs two mixture of normal distributions (Some minutes of search in statistical references turned into a failure). Consulting the original paper (Detecting bimodality in astronomical datasets by Ashman, Bird, and Zepf, 1994, AJ, 108(6), p. 2348-2361) and cited statistical references therein (for example, Mixture models: Inference and applications to clustering by McLachlan and Basford, 1988) may not have led such misuse of statistics.