In recent years there have been many reported detections of highly redshifted or blueshifted narrow spectral lines (both emission or absorption) in the X-ray spectra of active galaxies, but these are all modest detections in terms of their statistical significance. The aim of this paper is to review the issue of the significance of these detections and, in particular, take account of publication bias. A literature search revealed 38 reported detections of narrow, strongly shifted (v/c >= 0.05) X-ray lines in the 1.5-20 keV spectra of Seyfert galaxies and quasars. These published data show a close, linear relationship between the estimated line strength and its uncertainty, in the sense that better observations (with smaller uncertainties) only ever show the smallest lines. This result is consistent with many of the reported lines being false detections resulting from random fluctuations, drawn from a large body of data and filtered by publication bias such that only the most `significant fluctuations are ever reported. The reality of many of these features, and certainly their prevalence in the population at large, therefore remains an open question that is best settled though uniform analysis (and reporting) of higher quality observations.
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