2PCF binning bias introduced for a range of analysis choices, shown as the ratio between the measured and their proposed theoretical value as a function of angular scale, θ. The legends in this figure are shared between the two panels. For the weighted broad bin estimator, , the bias is calculated assuming θb is given by the logarithmic mid-point of the bin, θmid, log (green squares), the weighted mean of the bin, θw (black pluses, under the blue diamonds), the geometric mean or linear mid-point of the bin, θmid, lin (dark grey triangles), or an area-weighted bin centre, θarea (blue diamonds). These estimators can be compared to the fine binning case, , where the theory is estimated at the weighted mean of each bin (light grey circles), and the exact case (red crosses) where the theoretical value is calculated as a weighted integral over the signal within the bin (Eq. (A.7)). All points are plotted with errorbars, but in the case of broad binning the errors are too small to be visible.
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