Probability determined from the QML analysis for obtaining a dipole modulation amplitude at least as anomalous as the Commander (red), NILC (orange), SEVEM (green), and SMICA (blue) data sets, for the range ℓ ∈ [10,ℓ_max]. The vertical line corresponds to ℓ_max = 132 which was used as the search limit in Bennett et al. (2011). The probability grows approximately logarithmically with ℓ_max. This means that the adopted probability to exceed is fortunately not very sensitive to ℓ_max, and for any reasonable choice is above 10%.