FunChisq: Chi-Square and Exact Tests for Model-Free Functional Dependency

Statistical hypothesis testing methods for model-free functional dependency using asymptotic chi-square or exact distributions. Functional chi-squares are asymmetric and functionally optimal, unique from other related statistics. Tests in this package reveal evidence for causality based on the causality-by-functionality principle. They include asymptotic functional chi-square tests, an exact functional test, a comparative functional chi-square test, and also a comparative chi-square test. The normalized non-constant functional chi-square test was used by Best Performer NMSUSongLab in HPN-DREAM (DREAM8) Breast Cancer Network Inference Challenges. A function index derived from the functional chi-square offers a new effect size measure for the strength of function dependency, a better alternative to conditional entropy in many aspects. For continuous data, these tests offer an advantage over regression analysis when a parametric functional form cannot be assumed; for categorical data, they provide a novel means to assess directional dependency not possible with symmetrical Pearson's chi-square or Fisher's exact tests.

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