Abstract
While interest in Bayesian statistics has been growing in statistics education, the treatment of the topic is still inadequate in both textbooks and the classroom. Because so many fields of study lead to careers that involve a decision-making process requiring an understanding of Bayesian methods, it is becoming increasingly clear that Bayesian methods should be included in classes that cover the P value and Hypothesis Testing. We discuss several fallacies associated with the P value and Hypothesis Testing, including why Fisher’s P value and Neyman-Pearson’s Hypothesis Tests are incompatible with each other and cannot be combined to answer the question “What is the probability of the truth of one’s belief based on the evidence?” We go on to explain how the Minimum Bayes Factor can be used as an alternative to frequentist methods, and why the Bayesian approach results in more accurate, credible, and relevant test results when measuring the strength of the evidence. We conclude that educators must realize the importance of teaching the correct interpretation of Fisher’s P value and its alternative, the Bayesian approach, to students in an introductory statistics course.
Highlights
In recent years, Bayesian statistics has gone from being a controversial theory on the fringe of mainstream statistics to being widely accepted as a valuable alternative to more common classical approaches
Using P values, Hypothesis Tests, or the two combined to answer the main question of statistical inference is in many cases irrelevant and meaningless, because one is using deductive reasoning to answer an inductive-natured question
Contrary to what many believe, the combined method still cannot answer the question “What is the probability of the truth of one’s belief based on the evidence?” If the main goal of statistical inference is to answer that question, the combined method is not sufficient
Summary
Bayesian statistics has gone from being a controversial theory on the fringe of mainstream statistics to being widely accepted as a valuable alternative to more common classical approaches. Though not commonly, elementary statistics texts today are introducing Bayesian methods using Bayes’ Rule within a section on conditional probability (see for example, De Veaux, Velleman, & Bock, 2008; Sullivan, 2007; Triola, 2007; Larson & Farber, 2006; Bluman, 2004). Using P values, Hypothesis Tests, or the two combined to answer the main question of statistical inference is in many cases irrelevant and meaningless, because one is using deductive reasoning to answer an inductive-natured question. In the two sections of this paper we will discuss three frequentists approaches to statistical inference, followed by an introduction to an alternative inductive-natured statistical method called Bayesian methods
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
