We develop and apply a novel method of analysis to study the X-ray spectral properties of 908 QSOs in the Large Bright Quasar Survey (LBQS) that were observed during the soft X-ray ROSAT All-Sky Survey (RASS). Due to the relatively short (<600sec) RASS exposure times, only 10% of the QSOs are detected in X-rays, so X-ray spectral model fits for individual QSOs are precluded by poor photon statistics. Spectral stacking provides effectively much more sensitive X-ray observations for an average QSO in bins of redshift, and for several classes of QSOs. We model the stacked X-ray spectra in a way that obviates both the distinction between detections and non-detections, and the need to stack together only those objects observed through similar Galactic column densities N_H. In application to the LBQS/RASS sample, we marginally confirm a flattening of the X-ray spectral index of QSOs toward higher redshifts. Radio-loud QSOs show flatter X-ray photon indices, in agreement with previous work. We show that the apparent flattening of the photon index with redshift is not due to an increasing fractional contribution from the radio-loud class of QSOs.
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