ASSESSING ESTIMATION OF REGRESSION TO MEAN FOR NON-NORMAL POPULATIONS THROUGH TRANSFORMATIONS

Abstract

Regression to the mean is the phenomenon in which extreme values of a variable in one sample are discovered to be less extreme and more similar to the population mean following re-measurement. The first measurement is exceptional solely by accident. When individuals are chosen based on certain criteria or a cutoff point to determine the significance of an intervention effect, the observed change, known as the total effect, is made up of treatment and RTM effects. RTM must be taken into consideration in order to appropriately quantify the intervention effect. In this research, we aim to develop novel methods for estimating RTM effects in non-normal populations, transforming non-normal data into normal using Box-Cox transformations and bivariate normal data methods. The inverse transformation of RTM is then applied to bring it to the original units of the data. The second approach is motivated by the percentile change caused by the RTM, which is defined as the difference between the first quantile point and the mean of the data on the second occasion. The same amount of percentile change is used to identify the two quantile points whose difference is the RTM effect in that original population. We used several distributions to meet our research goals and evaluate the effectiveness of our proposed methods.