A signal present trial on which there is actual presentation of the target stimulus which is superimposed on the endogenous noise in the sensory system.( the stimulus is of one single low intensity)
Two responses are possible in the experiment: ‘yes’ indicates that an observer thinks a stimulus was present on a particular trial and ‘no’ indicates that the observer thinks the signal was absent.
The combination of two possible responses leads to four possible outcomes on a given trial. When the signal is present and the response is yes, the observer has made a hit. But if the observer responded yes when the signal was absent, then a false alarm has been made. When the observer doesn’t detect the signal when it is present it is called a miss and when the observer gives the response as no when the signal is not present then, it is called as correct rejection.
Eg: An experiment using the method of constant stimuli to measure two subjects’ thresholds for hearing a tone. The subjects have to say yes if they hear a tone and no if they don’t hear it.
Subject A knows that tones are presented on every trial and being supersensitive to tones says ‘yes’ to even the slightest possibility of hearing a tone.
Subject B who is not supersensitive to tones and wants to be sure before answering ‘yes’, will not say yes till the presented tone is strong.
The results of this experiment will show that subject A will give more yes responses than subject B and thus end up with a lower threshold. But this does not mean that subject A is more sensitive to tones than subject B. The lower threshold may be due to the reason that subject A is more willing to say yes to the tone than subject B. The difference between the two subjects is that each has a different response criterion.(RC) Subject A’s RC is low (as she will say yes if there is the slightest chance there is a tone present) whereas subject B’s RC is high (she says yes only when she is sure that she heard the tone)
This experiment shows that factors other than the subject’s sensitivity to the signal may influence the results of a psychophysical experiment.(in this case subject A’s willingness to say yes). This is the basis for signal detection theory, which says that there is a cognitive component to the subject’s responses while detecting a signal.
THEORETICAL BASIS
There are two basic theoretical explanations, for signal detection:
- The percentage of hits and false alarms depends on the subject’s criterion.
- A subject’s sensitivity to a stimulus is indicated by the shape of the subject’s ROC curve.
CONCEPTS IN SIGNAL DETECTION THEORY
There are two main concepts of signal detection theory:
Signal and noise
The signal is the stimulus presented to the subject. In the above eg. the signal was the tone.
The noise is all other stimuli in the environment, and since the signal is usually faint, noise can sometimes be mistaken for the signal. Eg: In the experiment mentioned above, hearing a tone on a trial in which no tone was presented is an example of auditory noise.
In the signal detection experiment, a signal is presented on some trials and no signal is presented on the other trials. Signal detection theory describes this procedure not in terms of presenting a signal or no signal but, in terms of presenting signal plus noise (S+N) or noise (N). It means that the noise is always present, and on some trials, we add a signal. A false alarm occurs if the subject says yes on a noise trial, and a hit occurs if the subject says yes on a signal-plus-noise trial.
Probability Distributions:
From the experiment, we know that when no stimulus is present, an observer’s sensory systems are still active, generating sensory noise. The amount of noise varies from moment to moment. This fluctuation in noise level can be caused by the operation of physiological, attentional and other variables on the sensory and perceptual systems of the observer. Signal detection theorists represent these fluctuations in the form of a probability distribution, which is a theoretical summary of many trials in an experiment.
10 20 30
In the graph, the probability distribution on the left represents the probability that a given perceptual effect will be caused by N and the one on the right represents the probability that a given perceptual effect will be caused by S+N. In the experiment, the probability distributions tell us what the chances are that the loudness of tone is due to N or S+N. If the subject hears a tone with a loudness of 10 on one of the trials of the experiment, we see that the probability that a loudness of 10 is due to N and if the tone has a perceived loudness of 30, it has a high probability of being caused by S+N. But, when the tone’s loudness is 20, it is equally probable that this loudness is due to N or S+N.
The Criterion
From the graph, we see that the signal is always accompanied by the noise. So, the subject in the experiment has to decide whether no tone (N) was present or whether a tone (S+N) was present. However, the overlap in the probability distributions for N and S+N makes this judgement difficult. According to the signal detection theory, the subject’s decision on detecting the signal depends on the location of the subject’s criterion, as sometimes the noise produces a sensation that is just as intense as that produced by the signal.
Criterion is the cutoff point for sensational level. This is the value we are willing to accept as indicating that a signal was most likely present.If we experience a sensation level (perceptual effect) below the criterion level we respond ‘no’. If it is above the criterion level, we respond ‘yes’.
There are three different criterions, which we adopt to respond on a given trial.
Liberal criterion:
In this criterion, the probability of saying yes when (N) is presented is high. And the probability of saying yes when the (S+N) is present is also high. So, this results in a high false alarm and a high hit.
Neutral criterion:
In this criterion, the probability of saying yes when (N) is presented is low and the probability of saying yes when (S+N) is presented is fairly high. This results in low false alarm and a fairly high hit rate.
Conservative criterion:
The false alarm will be very low when the (N) is present and hits will also be low, when the (S+N) is present.
According to the signal detection theory, the N and S+N distributions are very important as the sensitivity to a stimulus is indicated by the distance (d’) between the peaks of the N and S+N distributions and that this distance affects the shape of the ROC curve.