Commonly used statistical tests and their application

Abstract

The use of statistics to derive insights from the data has provided researchers with empirical tools to describe, diagnose, predict, and prescribe actions, interventions and generate knowledge from varied data sets. Depending on the types of data (structured, semi-structured, and unstructured), different statistical models and tests can be performed to generate the said insights and new knowledge. Correctly identifying the data types (whether the data is discrete or continuous) aids researchers in identifying the applicable statistical tests. The distribution of the data also has an implication for determining the relevant statistical test. When continuous data are said to be normally distributed, the types of tests that can be used to compare groups differ to when the data are found to be not normally distributed. The same is true for discrete data, in that there are certain assumptions that need to be satisfied to identify the correct statistical tests to use in comparing the data groups. In this paper, the discussion will be focused on nine commonly used statistical tests. These common tests include the t-test, paired t-test, analysis of variance (ANOVA) test, Wilcoxon rank sum test (WRST), Wilcoxon signed-rank test (WSRT), nonparametric ANOVA, chi-square (X²) test, Fisher's exact test, and McNemar's test. The conditions for the use of these tests will be described, and the applications thereof will be discussed. Therefore, the purpos of this paper is not to describe the mathematical theories behind different statistical tests but to introduce the tests and their applications.