A Bootstrap Common Mean Direction Test.

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. Plain Language Summary: Statistical inference is the process of using observations to infer the properties of an unobserved population. An example of this process in paleomagnetism (the study of Earth's ancient magnetic field based on information preserved in geological materials) is a test of whether two sets of field directions have a common mean. Traditional statistical methods used to address this question make assumptions about the properties of the observations, which are known to be invalid in many cases. An alternative approach is so‐called bootstrapping, which relaxes assumptions about the observations and can then be applied more widely. In this study, we show how bootstrapping can be applied to paleomagnetic observations within the interpretational structure of existing paleomagnetic statistics, thus, providing a consistent inference framework. Furthermore, using numerical experiments we investigate how many paleomagnetic observations are required for bootstrapping to yield reliable results. Key Points: Advances in bootstrapping directional data are consideredThe number of directions needed for bootstrap‐based inference is assessedA bootstrap common mean direction test (CMDT) for paleomagnetic directions is presented [ABSTRACT FROM AUTHOR]