Signals (stimuli) are always detected-whether by electronic devices or by humans-against a background of activity. The level of this background activity, called noise, is assumed to vary randomly and may be either external to the detecting device or caused by the device itself (e.g., physiological noise caused by spontaneous activity of the nervous system). In the detection situation, the observer must therefore first make an observation (x) and then make a decision about the observation. On each trial, the observer must decide whether x is due to a signal added to the noise background or to the noise alone. When a weak signal is applied, the decision becomes difficult, and errors are frequent. One factor contributing to the difficulty of the problem is the random variation of background noise. On some trials, the noise level may be so high as to be mistaken for a signal, and on other trials it may be so low that the addition of a weak signal is mistaken for noise. This state of affairs can
be represented graphically by two probability distributions describing the random variation of noise (N) and the signal plus noise (SN) (Figure 5.1). Since the signal is added to the noise, the average sensory observation magnitude will always be greater for the signal-plus-noise distribution, SN, than for the noise distribution, N. However, the difference between the means becomes smaller and smaller as the signal strength is decreased, until the distributions are essentially the same. It is when the two distributions greatly overlap that decision making becomes difficult.