Computing the Average Body Mass Index: A Study with Systematic Sampling Using Auxiliary Information

Abstract

Background. The use of body mass index (BMI) is prevalent, to measure the fat in the body. Sometimes, during a clinical survey, different measures of body parts of people may be available, but the actual weight and height are not available. In this article, we have shown a method to estimate the body mass index using the measures of different body parts. Systematic sampling is to be applied only if the given population is logically homogeneous because systematic sample units are uniformly distributed over the population. Methods. The method of estimation for the mean of the study variable under systematic sampling using auxiliary information has been used to estimate the body mass index (BMI). We also have shown the effect of observational error in the estimation. The measures of different body parts are taken as auxiliary variables. The correlation coefficient between BMI and the circumference of different body parts has been obtained. The efficacy of methods in terms of mean square error has been obtained in the estimation of BMI. Also, the observations available on different body parts are assumed to be recorded with observational error. Thus, we propose a method of estimation of BMI in the presence of observational error. A simulation study has been conducted to demonstrate the effect of the observational error on the estimation of body mass index. Results. The properties of the proposed estimation method have been derived under large sampling approximation, and the conditions under which the proposed method is more efficient are found. We assume the presence of observational error in the study of 252 men. The efficiency of the difference estimators is better in the presence of observational error. Also, the presence of observational error does not change the properties of the estimators. Conclusions. The study provides an easy approach and the simplest way to obtain the BMI estimation with and without observational error. Thus, the suggested method may be used by statisticians for this problem and for many other similar problems in the estimation of mean.