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We consider the distribution of many samples of Gamma-Ray Bursts (GRBs) whenplotted in a diagram with their bolometric fluence (Sbolo) versus the observedphoton energy of peak spectral flux (Epeak,obs). In this diagram, bursts thatobey the Amati relation must lie above some limiting line, althoughobservational scatter is expected to be substantial. We confirm that earlybursts with spectroscopic redshifts are consistent with this limit. But, wefind that the bursts from BATSE, Swift, Suzaku, and Konus are all greatly inviolation of the limit. In the Sbolo-Epeak,obs diagram, we find that everysatellite has a greatly different distribution. This requires that selectioneffects are dominating these distributions, which we identify. For detectorselections, the trigger threshold and the threshold to measure Epeak,obscombine to make a diagonal cutoff with the position of this cutoff varyinggreatly detector to detector. For selection effects due to the intrinsicproperties of the burst population, the distribution of Epeak,obs makes forbursts with low and high values to be rare, while the fluence distributionmakes bright bursts uncommon. For a poor threshold, the combination ofselection effects serves to allow only bursts within a region along the limitto be measured; these bursts will then appear to follow an Amati relation.Therefore, the Amati relation is an artifact of selection effects within theburst population and the detector. Therefore, the Amati relation should not beused for cosmological tasks. This failure is in no way prejudicial against theother luminosity relations.

A Significant Problem With Using the Amati Relation for Cosmological Purposes