Improvement of test for independence of multidimensional contingency table.

2016 Fiscal Year Final Research Report

• Project/Area Number: 24540133
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kagoshima University
• Principal Investigator: Taneichi Nobuhiro 鹿児島大学, 理工学域理学系, 教授 (00207200)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 多次元分割表 / 完全独立性検定 / 一要因対二要因独立性検定 / 条件付独立性 / エッジワース展開 / 変換統計量

Outline of Final Research Achievements

We consider multi-dimensional contingency table whose underlying distribution is assumed to be multinomial distribution. We improve the test for complete independence in contingency table of general dimension, test for one factor independence of the other two in three dimensional contingency table and test for conditional independence in three dimensional contingency table. To put it concretely, we constructed improved transformed statistics which are based on approximations of test statistics for independence by using Edgeworth expansion. When the statistic is the log-likelihood ratio statistic, the transformed statistic corresponds to Bartlett adjusted statistic. Nevertheless, the power of the test based on the transformed statistic is not so different from that of an original statistic, the transformed statistic improves the speed of convergence to chi-square distribution very well.

Free Research Field

数物系科学