Gamma-ray burst (GRB) satellites are relatively inefficient detectors of dim, hard bursts because they trigger on photon counts, which are number-biased against hard photons. Therefore, for example, given two bursts of identical peak luminosity near the detection threshold, a dim, soft burst will be preferentially detected over a dim, hard burst. This detector bias can create or skew an apparent correlation where increasingly hard GRBs appear increasingly bright. Although such correlations may be obfuscated by a middle step where GRBs need to be bright enough to have their actual redshifts determined, it is found that the bias is generally pervasive. This result is derived here through simulations convolving a wide variety of possible GRB brightnesses and spectra with the BATSE Large Area Detectors’ detection thresholds. The presented analyses indicate that the rest-frame νFν spectrum peak energy of long-duration GRBs, Ep, int, is not a good cosmological standard candle without significant corrections for selection effects. Therefore, the appearance of Ep, int in seeming correlations such as the Amati (Eiso–Ep, int), Ghirlanda (Eγ–Ep, int) and Liso–Ep, int relations is statistically real but strongly influenced by so far uncalibrated GRB detector thresholds.