The permutation framework is particularly well suited for inferential purposes as it allows one to do point estimation, confidence regions and hypothesis tests. The flipr package makes it easy and fun to perform all these inferential tasks within the permutation paradigm.
The central object is the so-called \(p\)-value function. The \(p\)-value function for a set of parameters \(\Theta\) is a curve that represents the variation of the \(p\)-value of an hypothesis test in which the null hypothesis is \(\Theta = \Theta_0\) as a function of \(\Theta_0\) (Martin 2017; Fraser 2019; Infanger and Schmidt-Trucksäss 2019).
Observe that, the non-parametric combination method available in the permutation framework (Pesarin and Salmaso 2010) allows you to infer multiple parameters at once. This means that you can natively compute a single confidence region for multiple parameters that controls the family-wise error rate by construction (think of a confidence region for both the mean and the variance for instance).
Version 0.2.1 of the flipr package released on CRAN features \(4\) main functions:
- You can compute \(p\)-value function when inferring multiple parameters at once via
two_sample_pf(); - You can compute a single point estimate for a single parameter of interest via
two_sample_pe(); - You can compute a confidence interval for a single parameter of interest via
two_sample_ci(); - You can automatically draw the \(p\)-value function for a single parameter of interest via
two_sample_viz().
This version also implements a number of small changes and bug fixes, the full list of which is available here.
Finally, a number of articles can be found on the dedicated website for flipr: https://astamm.github.io/flipr/. They explain in details how the permutation framework can be used for statistical inference and how flipr offers easy tools for making that happen seamlessly.