Statistical Analysis of Survey Data by Using Hypothesis Testing

Abstract

A common goal for a statistical research project is to investigate causality, and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response, there are two major types of causal statistical studies; experimental studies and observational studies. In both types of studies, the effect of differences of an independent variable (or variables) in the behavior of the dependent variable are observed. The term “chi-square” refers both to a statistical distribution and to a hypothesis testing procedure that produces a statistic that is approximately distributed as the chi-square distribution. Whether analyzing null-hypothesis is or not by using chi-square entirely depends on the significant level (alpha) and sample size. Whenever we make a decision based on a hypothesis test, we can never know whether or decision is correct. There are two kinds of mistakes we can make: (1) we can fail to accept the null hypothesis when it is indeed true (Type I error), or (2) we can accept the null hypothesis when it is indeed false (Type II error). This paper tries to reduce the chance of making either of these errors by adjusting between the significant level (alpha) and the minimum sample size needed.