Statistical Properties of Sampling Distributions of Different Test Statistics for Different Measures of Change and a New Test: Simulation Study

Abstract

The aim of this study is to analyse the distribution characteristics of four different test statistics, namely the Mean/Standard Error of Mean (Mean/SEmean), Median/Interquartile Range (Median/IQR), Trimmed Mean/Standard Error of Mean (TrMean/SEmean), and Trimmed Mean/Interquartile Range (TrMean/IQR), which can be used to test two measures of change, namely percent change (PC) and modified symmetrised percent change (MSPC). To ensure the selection of suitable test statistics using the two measures of change, the observed type-I errors and powers of the test statistics have been computed. Results demonstrate that the sampling distributions of the four different test statistics by using PC values exhibit skewness. The Mean/SEmean statistic for the MSPC measure exhibits a two-peak value and platykurtic distribution, while the TrMean/SEmean statistic shows a leptokurtic distribution. The Median/IQR test yields robust and powerful results, especially for large sample sizes. This new statistical measure is referred to as the HS test.