> On Aug 10, 2016, at 5:22 AM, Dominik Marti <d...@inik.ch> wrote: > > Hej R helpers > > The standard in statistical hypothesis testing is to reject the null > hypothesis that there is a difference between groups, i.e. to "prove" the > alternative. However, failing to reject the null hypothesis does not prove > it; its rejection just fails. > > Now, as stated in the article "Unicorns do exist: a tutorial on "proving" the > null hypothesis." by David L Streiner (Canadian Journal of Psychiatry, 48(11) > 2003), we can define the null hypothesis to be that there IS a difference > (exceeding a certain value, delta), the alternative hypothesis being that > there is none (or it is at least smaller than delta). If the data now manages > to reject the null hypothesis (of there being a difference exceeding delta), > we can say with a certain probability that there is none. > > Can I do this test in R? And if yes, any leads? > > (In my actual dataset I deal with paired data.) > > Best > Dominik
Bear in mind that we are not "proving" anything with statistics. There is still a level of uncertainty in everything we do. In the scenario above, you are, in essence, reversing the normal approach to testing a null versus alternative hypothesis. The null, in this case, is that there is a difference and the alternative being that there is none, within some pre-defined, acceptable, margin. In clinical studies, these are called "equivalence" studies or "bioequivalence" studies, a subset of which are called "non-inferiority" studies, which are one-sided versions. This is typically done, for example, when testing a generic version of a drug versus the pre-existing "brand name" version of the drug to demonstrate that they have equivalent efficacy and safety profiles, within a clinically acceptable range. There is at least one R package that is relevant, conveniently called "equivalence": https://cran.r-project.org/web/packages/equivalence/ that addresses these scenarios. Regards, Marc Schwartz ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
