Two-tier analysis in palaeomagnetism

Summary. The statistical analysis necessary for isolating the between-site dispersion in palaeomagnetic studies is presented, both for the case of a common within-site precision and for variable within-site precision.
Approximate distributions are derived for all the relavant statistics. It is shown that if it is necessary to perform a two-tier analysis the overall true mean direction should be estimated as the mean of individual site mean directions and an equation for the semi-angle of the cone of confidence about this mean direction is derived.
The last section of the paper lays out the process by which a two-tier analysis should be performed together with relevant equations.