Significance Level, Interpretation and Construction

Hypothesis testing is not set up so that a researcher can absolutely prove a null hypothesis. Rather, it is set up so that when a researcher does not find evidence against the null hypothesis, he or she fails to reject the null hypothesis. When the researcher does find strong enough evidence against the null hypothesis, he or she rejects the null hypothesis. This, although often confusing, is a subject with vast field of statistical application. In hypothesis testing, the significance level at some preassigned small value α is used to control the probability of Type I error (rejecting the null hypothesis when it is true), which is vital in building up theory and methods. Among many significance-level-related notions for interpretation and elements for construction of ...