GENERALIZING THE POINT BISERIAL TO MEASURE THE ASSOCIATION BETWEEN A SET OF DICHOTOMOUS VARIABLES AND A CONTINUOUS VARIABLE

Abstract

Exploring the statistical association between more than two variables requires utilizing a proper technique/test along with meeting its required assumptions. Measures of correlation are used to explain such associations by intervals ranging [0-1] or [-1-1], where values near one imply a strong positive relationship and vice versa. Numerous measures of association exist for variables with similar characteristics, such as nominal vs. nominal or ordinal vs. ordinal. However, only a handful of measures exploring the relationship between quantitative and qualitative variables are available. To the best of my knowledge, there is no available measure for measuring the association between a set of dichotomous variables and a continuous variable. Therefore, the present study aims to propose measures of association to evaluate the strength of the relationship between a set of dichotomous variables and a continuous variable, namely, mixed data. The proposed measures generalized the Point Biserial Correlation Coefficient for dichotomous variables with an identical or non-identical probability. The study utilized the Mean Square Error (MSE) and Bias as criteria for comparing the performance of the aforementioned measures of the association through extensive simulations and real data analyses. This study contributed by introducing association measures that can be applied to data from any field that depends in most cases on dichotomous variables and a continuous variable to study their association. However, it is a common phenomenon in the education sector. Therefore, the proposed measures applied to real datasets derived from the Education sector in Qatar. Education is an essential human virtue, a necessity of society, the basis of a good life, and a sign of freedom. Education is important for the integration of separate entities. Simulation study and real-data applications were carried out to compare the performances of the 𝜂2∗ , and the proposed measures based on MSE and bias considering different probabilities, sample sizes, correlation coefficients, and a different number of dichotomous variables. The research demonstrates that the two proposed measures had the best performances when the sample size and the number of dichotomous increased compared to 𝜂2∗