Box-Cox Transfromation and Bootstrapping Approach to One Sample T-Test

Abstract

One sample t-test is one of the most popular collections of statistical technique for analyzing data. Before we perform one sample T-Test the first thing that we should check is normality assumption. In this paper, we combine Box-Cox and bootstrapping idea in one algorithm. The purpose of Box-Cox is to ensure the data is normally distributed before the analysis. This combination is very useful for the modelling with an advanced analysis and perhaps can be an alternative method for modelling options in applied statistics scope. Through this combining method, we are capable to handle the case of non-normal data and small and limited sample size data by bootstrapping the original data set to generate new ones. In our case, the term “bootstrap” actually is referring to the use of the original data set to generate new ones. In this research paper, from a small and limited sample size data, we performed bootstrapping method in order to generate a new data set with a bigger sample size. After getting a new sample size, we then perform one sample T-Test using standard procedures and modified procedure. Results from both analyses will be compared with others to know the efficiency of the modified procedure. We also provided some example of application of the method discussed by using SAS language computer software.