Hypothesis Tests, Confidence Intervals And Common Sense


Book: 
Proceedings of the sixth international conference on teaching statistics, Developing a statistically literate society
Authors: 
O'Brien, T. E.
Editors: 
Phillips, B.
Category: 
Pages: 
Online
Year: 
2002
Publisher: 
International Statistical Institute
URL: 
http://www.stat.auckland.ac.nz/~iase/publications/1/3m3_obri.pdf
Abstract: 

Applied researchers are often interested in obtaining confidence intervals for key nonlinear model parameters so as to answer important research questions, and the usual "plus and minus 2 SE's" confidence interval leads easily into the usual Wald hypothesis test covered in most introductory statistics courses. However, since information about a specific parameter is often asymmetric, a skewed confidence interval is often more appropriate and reasonable in practice. This leads to the use of likelihood-based tests, typically introduced in intermediate undergraduate and basic graduate course. This paper argues that the superiority (in terms of for example increased power) of likelihood-based and score hypothesis tests over the Wald test is most easily conveyed and appreciated by first providing a reasonable motivation (as well as examples) using confidence intervals, and then exploiting the confidence interval-hypothesis test equivalence.