'Statistics Gone on Holiday': Misinterpretations of Hypothesis Tests Propagated by Internet Resources

Journal of Social Science and Humanities, Vol 5, No. 3, 2019 http://www.aiscience.org/journal/allissues/jssh.html?issueId=70320503

9 Pages Posted: 19 Jan 2017 Last revised: 7 Jan 2021

See all articles by Chris Thron

Chris Thron

Texas A&M University (TAMU), Central Texas

Nancy Hernandez

Texas A&M University (TAMU), Central Texas

Date Written: June 1, 2019

Abstract

“Type I error” is a basic concept in statistical hypothesis testing. However, the term is used in two subtly different senses in statistics texts and other statistical literature. Specifically, type I error can be construed either as a conditional event (i.e. presuming that the null hypothesis is true) or an unconditional event. We explain the distinctions between the different usages of type I error, and we conduct a logical analysis of popular statistics web sites to determine their usage of the terminology. Our analysis shows that ambiguous and inconsistent usage of this terminology leads to wrong interpretations of significance level in many web pages, leading in turn to faulty interpretations of the results of experiments. We discuss the reasons for this long-standing lack of consensus in the definition of type I error. The unconditional-event definition is more intuitive and agrees with the original formulation Neyman and Pearson in 1933, but professional statisticians favor the conditional-event definition. The fact that users of statistics come from widely different fields makes it difficult to arrive at a single agreed-upon definition. We conclude that even in a rigorous technical subject like statistics, ambiguous terminology can go unrecognized and can continue to produce errors in reasoning.

Keywords: Conditional probability, hypothesis testing, significance level, Type I error, web pages, internet, statistical concepts

JEL Classification: C12, C18

Suggested Citation

Thron, Christopher and Hernandez, Nancy, 'Statistics Gone on Holiday': Misinterpretations of Hypothesis Tests Propagated by Internet Resources (June 1, 2019). Journal of Social Science and Humanities, Vol 5, No. 3, 2019 http://www.aiscience.org/journal/allissues/jssh.html?issueId=70320503, Available at SSRN: https://ssrn.com/abstract=2817863 or http://dx.doi.org/10.2139/ssrn.2817863

Christopher Thron (Contact Author)

Texas A&M University (TAMU), Central Texas ( email )

1001 Leadership Place
Killeen, TX 76549
United States

Nancy Hernandez

Texas A&M University (TAMU), Central Texas ( email )

1001 Leadership Place
Killeen, TX 76549
United States

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