Mean weighted residuals reveal systematic overestimation of Bragg intensities in single-crystal diffraction

The mean value of weighted residuals (〈ζ〉) was analysed for 8424 published single-crystal X-ray data sets of crystals containing only light elements (C, H, N, O). A striking asymmetry was observed: 71.5% of data sets exhibit positive 〈ζ〉 values, occurring 2.5 times more often than negative values. This imbalance suggests systematic errors, with evidence pointing to a slight overestimation of observed intensities (I _obs). Simulations and theoretical analysis show that such overestimation artificially lowers common data-quality metrics, including the popular merging factor R _merge, the redundancy independent factor R _r.i.m., the precision indicating factor R _p.i.m., the weighted agreement factor wR(F ²) and even atomic displacement parameters, creating a 'rewarding error' that may reinforce confirmation bias. Experimental data confirm these findings, as residual factors reach their minima for 〈ζ〉 > 0 rather than at zero. These results highlight the need for critical evaluation of data-processing strategies and caution against relying solely on conventional agreement factors as indicators of accuracy.