The LMS for testing independence in two-way contingency tables

Abstract

SummaryIn the statistical literature there are proposed many test measures to determine the independence of two qualitative variables in contingency tables, in particular in two-way contingency tables larger than 2×2. For statistical analysis, three of the so-called “chi-squared tests”—the T3 test, BP test and |χ| test—were selected. These tests were compared with a logarithmic minimum test, which is the author’s proposal. Critical values for the tests were determined with the Monte Carlo method. To compare the tests, an appropriate measure of untruthfulness of H0 was used and the power of the tests was calculated.

Test of Association in the Presence of Complex Environment

“…Dutton et al [6,7] discussed the application of the test in education. More applications of the test can be seen in [8][9][10][11][12][13][14][15][16][17].…”

Non-informative nuisance parameter principle for weighted likelihood test using adaptive significance levels in count data

“…When these procedures deal with small samples sizes or sparsity (cells counts close to zero), their performances are very poor, as we can see in the LRT test (Table 3 -11). Although some modifications have been made (see, for example, Sulewski (2019) and their references), there is not a complete solution yet. From a Bayesian perspective, there is a wide literature on methods for analyzing data with contingency tables (Agresti and David (2005); Lindley and Smith (1972)).…”