Pattern Analysis Across Contingency Tables
Statistical hypothesis testing of pattern heterogeneity
via differences in underlying distributions across multiple
contingency tables. Five tests are included: the comparative
chi-squared test (Song et al. 2014) <10.1093>
(Zhang et al. 2015) <10.1093>, the Sharma-Song
test (Sharma et al. 2021) <10.1093>,
the heterogeneity test, the marginal-change test (Sharma et al.
2020) <10.1145>, and the strength test
(Sharma et al. 2020) <10.1145>. Under the
null hypothesis that row and column variables are statistically
independent and joint distributions are equal, their test
statistics all follow an asymptotically chi-squared distribution.
A comprehensive type analysis categorizes the relation among the
contingency tables into type null, 0, 1, and 2 (Sharma et al.
2020) <10.1145>. They can identify
heterogeneous patterns that differ in either the first order
(marginal) or the second order (differential departure from
independence). Second-order differences reveal more
fundamental changes than first-order differences across