Statistical Relationship between Quantitative and Dichotomous Variables: Student’s Test and Moving Average Approach

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Varaksin Anatoly Nikolaevich; Maslakova Tatiana Anatolyevna; Konstantinova Ekaterina Danilovna; Shalaumova Yulia Valeryevna

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Journal Paper

Paper Information

Journal: JOURNAL OF THE IRANIAN STATISTICAL SOCIETY Year:2023 | Volume:22 | Issue:1 Page(s): 123-135

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Title

Statistical Relationship between Quantitative and Dichotomous Variables: Student’s Test and Moving Average Approach

Author(s)

Varaksin Anatoly Nikolaevich | Maslakova Tatiana Anatolyevna | Konstantinova Ekaterina Danilovna | Shalaumova Yulia Valeryevna | Issue Writer Certificate

Keywords

Analysis of variance

Body Mass Index

linear regression

Moving average

Smoking

Stress Index

Student’s Test

Quantitative Predictor and Dichotomous Outcome

Abstract

A new technique is proposed for evaluating the statistical relationship between a quantitative variable Y and a dichotomous variable X assuming two values: X=0 and X=1. The technique is based on the division of the quantitative variable Y into strata by the moving average technique and computation of average values in the strata for the variables Y and X. Stratification turns the dichotomous variable X into a quantitative one. Once the variable X has been transformed in this way, the statistical relationship between Y and X may be analyzed by linear regression and by analysis of variance. Thus, the technique proposed expands the range of methods available for analyzing statistical relationships between quantitative and dichotomous variables. Specific examples are used to compare the moving average technique with the t-test for symmetric (normal) and asymmetric distributions of quantitative variable Y. It is shown that the statistical relationship between stratified Y and X can be strongly different for a symmetrically (normally) distributed variable Y.

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