Everything You Wanted to Know but Could Never Find from the Cochran-Mantel-Haenszel Test  

作　　者：José Moral de la Rubia Adrián Valle de la O José Moral de la Rubia;Adrián Valle de la O(School of Psychology, Universidad Autónoma de Nuevo León, Nuevo León, Monterrey, Mexico;School of Medicine and Health Science, Tecnológico de Monterrey, Monterrey, Mexico)

机构地区：[1]School of Psychology, Universidad Autónoma de Nuevo León, Nuevo León, Monterrey, Mexico [2]School of Medicine and Health Science, Tecnológico de Monterrey, Monterrey, Mexico

出　　处：《Journal of Data Analysis and Information Processing》2023年第3期310-339,共30页数据分析和信息处理（英文）

摘　　要：The Cochran-Mantel-Haenszel (CMH) test, developed in the 1950s, is a classic in health research, especially in epidemiology and other fields in which dichotomous and polytomous variables are frequent. This nonparametric test makes it possible to measure and check the effect of an antecedent variable X on a health outcome Y, statistically controlling the effect of a third variable Z that acts as a confounding variable in the relationship between X and Y. Both X and Y are measured on a dichotomous qualitative scale and Z on a polytomous-qualitative or ordinal scale. It is assumed that the effect of X on Y is homogeneous between the k strata of Z, which is usually tested by the Breslow-Day test with the Tarone’s correction or the Woolf’s test. The main statistical programs have the CMH test together with a test to verify the assumption of a homogeneous effect across the strata, so that it is easy to apply. However, its fundamentals and details of calculations are a mystery to most researchers, and even difficult to find or understand. The aim of this article is to present these details in a clear and concise way, including the assumptions and alternatives to non-compliance. This technical knowledge is applied to a simulated realistic example of the area of epidemiology in health and, finally, an interpretive synthesis of the analyses is given. In addition, some suggestions for the test report are made.The Cochran-Mantel-Haenszel (CMH) test, developed in the 1950s, is a classic in health research, especially in epidemiology and other fields in which dichotomous and polytomous variables are frequent. This nonparametric test makes it possible to measure and check the effect of an antecedent variable X on a health outcome Y, statistically controlling the effect of a third variable Z that acts as a confounding variable in the relationship between X and Y. Both X and Y are measured on a dichotomous qualitative scale and Z on a polytomous-qualitative or ordinal scale. It is assumed that the effect of X on Y is homogeneous between the k strata of Z, which is usually tested by the Breslow-Day test with the Tarone’s correction or the Woolf’s test. The main statistical programs have the CMH test together with a test to verify the assumption of a homogeneous effect across the strata, so that it is easy to apply. However, its fundamentals and details of calculations are a mystery to most researchers, and even difficult to find or understand. The aim of this article is to present these details in a clear and concise way, including the assumptions and alternatives to non-compliance. This technical knowledge is applied to a simulated realistic example of the area of epidemiology in health and, finally, an interpretive synthesis of the analyses is given. In addition, some suggestions for the test report are made.

关 键 词：Odds Ratio Effect Size Statistical Control Qualitative Variables Nonparametric Statistics 

分 类 号：O17[理学—数学]