A Bootstrap Common Mean Direction Test

Abstract

Paleomagnetic statistical inference is underpinned by a family of parametric null hypothesis tests. In many cases, however, paleomagnetic data do not meet the distributional assumptions of these tests, which can lead to spurious inferences. Earlier studies have proposed the bootstrap as a nonparametric alternative for paleomagnetic analysis, which can be applied even when the distributional form of the data is unknown. Key among these approaches is the bootstrap test for a common mean direction, which relies on assessment of the overlap of estimated confidence regions. In its current form, the bootstrap test for a common mean paleomagnetic direction does not consider a null hypothesis and can yield outcomes that cannot be interpreted in terms of a statistical significance level. To resolve these issues, we use recent advances to place such bootstrap tests within a null hypothesis significance testing framework, and unify them with the existing family of paleomagnetic statistical tests. Furthermore, using numerical experiments we demonstrate the applicability of such a nonparametric approach to moderately sized paleomagnetic data sets typical of modern and legacy studies. Finally, we demonstrate how a confidence region can be estimated for the common mean of two sets of directions and how known directions, such as the expected field produced by a geocentric axial dipole, can be compared to that mean.