|Timothy E. O'Brien (USA)||firstname.lastname@example.org|
|Biomedical researchers, agronomists
and econometricians are often interested in obtaining confidence intervals
for key nonlinear model parameters so as to answer important research questions
and thus provide a natural introduction to and motivation for hypothesis
testing. As such, the introduction of confidence intervals as a means of
performing hypothesis testing is crucial, and the usual "plus and minus
2 SE's" confidence interval leads easily into the usual Wald hypothesis
test covered in most introductory (undergraduate) courses in statistics.
Extensions of these methods are rarely necessary for students enrolled in
very basic statistics courses.
Since information about a given attribute or parameter is often asymmetric, a skewed confidence interval may be more appropriate and reasonable. This leads to the use of likelihood-based tests, typically introduced in intermediate undergraduate and basic graduate courses, which are thus more suitable in practice. The superiority, in terms of, for example, increased power, of likelihood-based and score hypothesis tests over the Wald test is most easily motivated and appreciated via the confidence interval-hypothesis test approach.
This paper discusses the experiences of the author in teaching basic and intermediate biostatistics courses to pre-med students enrolled as Biology majors and Biostatistics minors. Examples are provided in which Wald and profile-likelihood intervals lead to opposing decisions, which can lead statistical educators into a heuristic discussion of curvature. Implications for design of experiments are discussed in the light of concurrent medications for HIV. This simple example serves to tie together disparate concepts from courses in statistical theory (estimation, testing, power), statistical methods (categorical data analysis, nonlinear regression), differential geometry (statistical curvature), statistical computing (convergence algorithms), and experimental design, helping intermediate students to make connections and see the larger picture.
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