While the Minimum Euclidean Distance detection is known to be optimal for channels affected by Gaussian noise, it has been shown that Minimum Pearson Distance detection (MPD) may perform better when the channel is also affected by an unknown offset, though for a good performance some adaptations for classical binary block codes are necessary. It is shown for cosets of first order Reed-Muller codes R(1,m) containing words of weight d/2, where d is the code's distance, that the minimum Pearson distance is always low for m≤4. However, it is possible to find cosets where the minimum Pearson distance is higher for m≥5.