A common conceptualization of signal detection theory (SDT) holds that if the effect of an experimental manipulation is truly perceptual, then it will necessarily be reflected in a change in d' rather than a change in the measure of response bias. Thus, if an experimental manipulation affects the measure of bias, but not d', then it is safe to conclude that the manipulation in question did not affect perception but instead affected the placement of the internal decision criterion. However, the opposite may be true: an effect on perception may affect measured bias while having no effect on d'. To illustrate this point, we expound how signal detection measures are calculated and show how all biases—including perceptual biases—can exert their effects on the criterion measure rather than on d'. While d' can provide evidence for a perceptual effect, an effect solely on the criterion measure can also arise from a perceptual effect. We further support this conclusion using simulations to demonstrate that the Müller-Lyer illusion, which is a classic visual illusion that creates a powerful perceptual effect on the apparent length of a line, influences the criterion measure without influencing d'. For discrimination experiments, SDT is effective at discriminating between sensitivity and bias but cannot by itself determine the underlying source of the bias, be it perceptual or response based.