Statistics and Its Interface

Volume 11 (2018)

Number 2

Testing the equality of risk difference among multiple incomplete two-way contingency tables

Pages: 353 – 368



Huiqiong Li (Department of Statistics, Yunnan University, Kunming, China)

Niansheng Tang (Department of Statistics, Yunnan University, Kunming, China)

Guoliang Tian (Department of Mathematics, Southern University of Science and Technology, Shenzhen, China)

Hongyuan Cao (Department of Statistics, University of Missouri, Columbia, Missouri, U.S.A.)


Contingency tables are used to summarize categorical data with multiple attributes, which frequently arise in natural and social sciences. In Tian and Li (2015), the equality of risk difference based on a $2 \times 2$ table is tested at the presence of non-response. In this paper, we derive the joint distribution of multiple contingency tables with non-response. Consequently, we propose a new homogeneity test statistic for the risk difference among multiple contingency tables. The limiting distribution of the proposed test statistic is established along with inferential procedures. Upon rejection of the global null hypothesis of homogeneity, to identify contingency tables with discordance, a multiple comparison procedure is proposed. Numerical studies corroborate theoretical results. We illustrate our method with dataset from a psychiatric study.


hypothesis testing, incomplete contingency table, risk difference

2010 Mathematics Subject Classification

Primary 62H17. Secondary 62H15.

The research of Hongyuan Cao was partially supported by the National Natural Science Foundation of China (No. 11561075).

The research of Huiqiong Li, Niansheng Tang, and Hongyuan Cao was partially supported by the Science Foundation of Yunnan Province (2016FB005).

Received 1 February 2017

Published 7 March 2018