Angular separation between the best-fit dipoles derived from different relations, without (top) and with (bottom) injected scatter. Linestyles indicate statistical methods: solid for MCMC; dashed and dash-dotted for the M21 method, differing slightly in implementation. Dashed lines define the dipole by highest significance (our default for the M21 method); dash-dotted lines by highest amplitude. The two give nearly identical results. The grey line indicates the expected distribution for uncorrelated dipoles.