Further considerations of TSD CHAPTER 6, Psychophysics the Fundamentals
Testing the assumptions of the theory of signal detection Low threshold theory Status of threshold concept
Testing the assumptions of the theory of signal detection The form of the ROC curve predicted from TSD can be more easily subjected to experimental tests if the hit rates and false alarm rates obtained in an experiment are plotted on the ROC curve as z scores.
If the N and SN distributions are normal in form and also have equal variances, the ROC curves should be linear with a slope of 1.0. Figure 6.1
The standard procedure is to determine the best fitting straight line for the data plotted as z scores. If the data points do not significantly deviate from the function, the assumption of normal distribution is supported.
However, the assumption that the N and SN distributions have equal variances is often not true. The slope of ROC curve is frequently found to be less than 1.0. variance is greater for the SN than the N distribution δsn/δn= 1/slope of Z score ROC curve
The standard deviation of the SN distribution is twice as large as the standard deviation of the N distribution.
The symbol ∆m, rather than d’, is some times used the denote the difference between the means of normal N and normal SN distributions.
∆m However, that for observer 2 the value of d’ is not constant along the ROC curve. The value of ∆m is equal to the absolute difference between Zsnand Zn at the point where Zsn is equal to 0.
de’ A measure of signal detectability that is sometimes used instead of ∆ m is de’. The value of de’ is the absolute difference between Zn and Zsn at a point on the ROC curve where it crosses the diagonal with negative slope. The primary benefit of using de’ is that it gives equal weight to δn and δsn.
da A third measure of signal detectability used when the variances of the N and SN distributions are unequal is da. The measure de’ and da specifies signal detectability in terms of units that represent the average of the standard deviations of the N and SN distributions.
da d’e the detectability of the signal is expressed in terms of the arithmetic average of the standard deviation of the N and SN distributions. da expressed signal detectability in terms of root-mean-square average of the squared standard deviation of the N and SN. da=b/(0.5√1+s2)
p(A) p(A): the proportion of the area of the entire graph that lies beneath the ROC curve.
p(A) There are two feature of p(A) that make it a highly useful measure of signal detectability. First p(A)is define without regard to underlying distributions. Z(a)=s(∆m)/√1+s2 Second, it is equivalent to p(c), the proportion correct in a two-alternative force-choice task.
Low threshold theory In low threshold theory, some of the false alarms on catch trials are due to an observation being above threshold, while others are due to guessing when the observation is below threshold.
Luce(1963) proposed another version of low threshold theory. The threshold is assumed to exist somewhere between the middle and the upper end of the noise distribution. In this theory, observations above threshold are also assumed to be indiscriminable from another.
Observers can discriminable between two kinds of sensory events.
Observer thresholds, which are inferred from the analysis of detection judgments, primarily through examination of the forms of ROC curves, are not to be confused with psychological energy thresholds measured by various psychophysical methods.
Gescheider illustrate an energy thresholds… Fig6.9
The energy threshold is not tied to the assumption that there is a boundary on the continuum of sensory magnitude below which events cannot be discriminated and above which events can be discriminated.
Vendrik and Eijkman found that the probability of detecting mechanical and electrical stimulus on the skin does not change until a certain stimulus strength is exceeded. Vendrik and Eijkman concluded: the temperature sensory system doesn’t have a measureable threshold, while both the tactile system and the system stimulated by electrical current do have energy threshold.
The hypothesis that the sense of touch has an energy threshold has gained strong support from studies in which it has been possible to record neural activity from coetaneous nerve fibers of humans.
Hamer : observers detected vibro-tactile stimulus in the presence and in the absence of background stimulus.
Hamer hypothesized that, for the test stimulus to be detected, its intensity must exceed a threshold in the receptor for generating action potentials.
Status of the threshold concept Observer threshold occur only when it is possible to demonstrate that observer’s nervous system is capable of being in two different states. Energy threshold occur only when it is possible to demonstrate that observer’s performance is the same in the presence of as in the absence of a weak signal.
Empirical threshold may be defined as the intensity of the signal needed to produce some specified level of performance by the observer.