Jon Faust
mostly economics


 Flower explained

Rejection regions

The figure shows the unit sphere with (0,0,0) at the center. The center of the flower is on the ray from the origin through (1,1,1).

Since the conventional t-test of the null hypothesis that the mean is zero is scale invariant, we can represent test rejection regions for samples of three observations as regions on the surface of the unit sphere. The purple circle is the rejection region of a the t-test with nominal size 3/14 and the critical value taken from the t distribution. The blue flower is the rejection region with the same nominal size but with the critical region determined by the population limit of the standard, percentile-t, bootstrap.

Note: Thanks to Jonathan Halket and Sergey Chernenko for help on the research leading to picture.