a) Histograms of 1000 dipoles measured from ten simulated filtered maps for the W1 DA. For each map, dipoles were computed placing the template at 100 random positions. The solid black and blue lines show the results obtained for the template of real clusters, T1, and for the simulated template of randomly positioned clusters, S1, respectively. For comparison, the solid red line shows the distribution of 360 dipoles computed by rotating the T1 template on a simulated map. b) As a) but focusing on the 3−5.5  μk range and showing the R1 renormalized to a total of 1000 to facilitate the comparison of the three error estimators. Panels c) and d) show the distribution of the dipole directions in Galactic coordinates. In all panels, the vertical dot-dashed line represents the measured dipole according to Kashlinsky et al. (2010).