A person that shall remain nameless asked me to write a “signal detection theory for dummies” blog post as my next feature. At first, I sighed (although that’s probably because I sigh a lot); then, I thought it’d be too much work and I did not want to do it; and finally, I am here typing away. So, let’s see how this goes*.
Detection theory has been used in Cognitive Psychology (and presumably other areas of psychology as well) since at least the appearance of Signal Detection Theory and Psychophysics by Green and Swets [Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics (Vol. 1). New York: Wiley]. Legend has it that signal detection theory emerged from radar engineering, and specifically from the necessity of distinguishing enemy boats/planes/missiles from random blips on the radar screen (actually, blimps from blips would work better). Just imagine some old, dark green, radar monitor: anything that appears on the screen could either be a missile (in this case, signal) or just visual noise that poses no threat – before the days of high definition, monitors would have quite a lot of visual disturbances. Since blips and blimps look very similar on the radar screen, telling noise from signal is not a straightforward task – here comes the need for a decision. Of course, when faced with the task of telling blips from blimps, Mr Radar Operator does not know whether the stimulus is one or the other. On what basis, then, can Mr O. make his decision?
One way we can think of the problem is to assume that there is an underlying dimension that represents signal strength: blimps will have on average more signal strength than blips, since they are actual signals. We can call this dimension blimpness for the time being. If we put this dimension on the x-axis and frequency of occurrence on the y-axis, and we assume normal distribution for both blimps’ (Signal) and blips’ (Noise) blimpness, then we should see something like this (see Figure below).
In our figure, blimpness (or signal strength) increases as we move right, so that at the extreme left of the blimpness axis we have very little blimpness, whereas at the extreme right we have a lot of it. Following this logic, we can then have two distributions of stimuli. The actual blimps, the signal stimuli, will be on average higher in signal strength than the screen blips, representing noise. For this reason, the signal distribution appears to be positioned to the right of the noise distribution. Of course, psychologically speaking, these distributions do not just magically pop up into our heads. We still have to make an actual decision as to whether a stimulus is a blip or a blimp. What we rely upon for our decision is how much signal strength we perceive for each stimulus. In general, and based on the figure above, we would expect that blimps have higher average signal strength than blips.
Exploring the figure a bit more, you will notice that there is also an area of overlap between the two distributions. That area is really the main decisional problem, since the discrimination between blimps and blips becomes harder when the difference in signal strength is less and, essentially, a distinction becomes more ambiguous.
We can think about it in the following terms. Imagine that, like in the figure below, you have three stimuli appearing on your radar screen. Stimulus 1 is larger and darker than stimulus 2, which in turn is larger and darker than stimulus 3. Therefore, in this example, signal strength is highest for 1, medium for 2 and lowest for 3. We can easily imagine 1 to be a blimp and it will fall somewhere within the the signal distribution on the right-hand side of the graph.
Analogously, we can imagine 3 to be a blip and to fall within the the noise distribution on the left. The problem is 2. Stimulus 2 is more ambiguous, being less clearly defined, and therefore poses a bigger decisional problem: is it signal or noise? is it a blip or a blimp?
A key tenet of signal detection theory is that the observer sets a decisional criterion that will help them make the decision. If we go back to the first figure, we see a line cutting the distributions right in the middle of where they intersect. This line represents a criterion. The basic idea here is that the observer will set a certain amount of signal strength as the threshold for their decision: if I perceive the strength to be at or above this criterion, then I will call the stimulus a blimp, otherwise, I will call the stimulus a blip.
As you can also appreciate from the first figure, the criterion is not an immovable object, but rather a flexible tool. The criterion can be shifted to the left, as indicated by the left arrow in the Figure, or can be shifted to the right, as per the right arrow. This idea of a movable criterion is quite important. A criterion that lies to the left of the intersection is typically considered to be a liberal criterion; this is because the observer requires less signal strength, or less evidence, before calling a stimulus a blimp. In other words, the observer is here quite liberal with the use of the B-word. In contrast, if an observer sets a conservative criterion, she/he sets a criterion that lies to the right of the intersection. In this case, the observer is much more careful with what they call a blimp – much stricter in their decisions.
And this is signal detection theory in a nutshell. Obviously, there is much more to it than what I wrote, but these are the basic ideas. If you want to read more, I can recommend the book referenced in *, of course, together with the Long-term Memory chapter I contributed to for Cognitive Psychology (here), and a couple of journal papers: Bruno et al. (2009) – which is available here – , and Higham et al. (2009) – which you can also find here.
In the next few posts, I will talk about two papers that I currently have in press, where signal detection theory was applied to the detection of liars, and to testing the gaydar.
*Full disclosure – Detection Theory by Macmillan and Creelman (Macmillan, N. A., & Creelman, C. D. (2004). Detection theory: A user’s guide. Psychology press) is permanently on my desk, but that may have a lot to do with lack of shelf space. As a second piece of disclosure, I have worked for a time** in Caren Rotello’s lab at UMass, where Neil Macmillan was a regular presence, oozing wisdom by the bucketful.
** I know that to be true because my photo is on the website. Incidentally, that photo was taken while I was at the University of Southampton (not at UMass) and is probably being used with no permission. Not that that is the problem. The problem is that, on the day of the photo shoot, I turned up not remembering that there was going to be a photo shoot, and so now I am permanently depicted wearing a Ramones hoodie and a Superman kiss curl.