Statistical tests under Dallal's model: Asymptotic and exact methods

Zhiming Li; Changxing Ma; Mingyao Ai

doi:10.1371/journal.pone.0242722

Statistical tests under Dallal's model: Asymptotic and exact methods

PLoS One. 2020 Nov 30;15(11):e0242722. doi: 10.1371/journal.pone.0242722. eCollection 2020.

Authors

Zhiming Li¹, Changxing Ma², Mingyao Ai³

Affiliations

¹ College of Mathematics and System Science, Xinjiang University, Urumqi, China.
² Department of Biostatistics, University at Buffalo, Buffalo, NY, United States of America.
³ LMAM, School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing, China.

Abstract

This paper proposes asymptotic and exact methods for testing the equality of correlations for multiple bilateral data under Dallal's model. Three asymptotic test statistics are derived for large samples. Since they are not applicable to small data, several conditional and unconditional exact methods are proposed based on these three statistics. Numerical studies are conducted to compare all these methods with regard to type I error rates (TIEs) and powers. The results show that the asymptotic score test is the most robust, and two exact tests have satisfactory TIEs and powers. Some real examples are provided to illustrate the effectiveness of these tests.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Models, Statistical*

Grants and funding

This research is supported by the National Natural Science Foundation of China (Grant Nos: 12061070, 12071014, 11661076), and the Science and Technology Department of Xinjiang Uygur Autonomous Region (Grant No: 2018Q011).