Sensitivity of Data Scale on Mean Value Test.

Abstract

In many surveys, researchers have often to deal with qualitative or categorical measurements. Sometimes, even continuous objects or characteristics have to be measured by using a discrete scale. It may be caused by the inability of researchers to perform measurements or scoring of an object precisely using continuous scale. This will reduce the degree of accuracy of the actual conditions of the measurement results. Therefore, it can imply bias in the results of statistical tests performed. This research is intended to measure the bias of T-test on categorical data based on various sample sizes and data distributions. Moreover, this research aims to determine the optimal combination between the number of categories and the number of sample size to produce a certain bias. This study focuses on the statistical test to compare the characteristics between two groups or populations. The bias is measured as a margin of error of the confidence interval. Preliminary data are generated by a computer program and then they are split into two to fifteen categories on the same interval. The results of the study are as follows. For normally and Poisson distributed data, increasing number of categories or sample size will imply decreasing average margin of error. An explicit bias function according to sample size and category has been proposed. Categorization of data can increase the bias in the confidence interval, but fortunately the bias doesn’t change the conclusion of the -test.