Signal Detection Theory: Basics

The figure below illustrates how signal detection theory conceives of what is going on inside of the nervous system during the detection of a faint or confusing stimulus or signal.  When the signal is not present, the activity in the nervous system is not always the same.  There are random variations.  This aspect of our functioning is indicated by the blue line.  It is our old friend the normal or bell-shaped curve.  It has a mean strength and a standard deviation given arbitrary values below.  This situation is the mess or noise that confuses the detection.  When the signal is present, the curve moves to the right on the graph because the signals adds a constant value on to the noise.  This situation is indicated by the purplish curve, the Signal + Noise curve, below.  It is also a normal curve with the same standard deviation, just moved to the right.  Now remember, the higher the curve the more likely that value of sensory strength is to occur.  However, any part of the sensory strength axis under a curve can occur.


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Looking at the two curves you notice that as they are initially set up here, the overlap a great deal which means that for many sensory experience intensities, it could be caused by either the noise alone or the signal plus the noise.  This is why they are confusing.  How confusing is indicated by a measure called d' (pronounced d-prime).  The larger d' the farther apart the two curves and the easier to tell signal from noise.  The size of d' depends upon the strength of the signal or stimulus.  This measure, d', is often called a measure of the sensitivity of the person to the signal.  The other thing to notice is the value called Beta.  It is a cutoff value set up by the subjects decision.  If the sensory strength is stronger than beta, then the person will report the signal as present.  If less than beta, the person will report the signal as absent.  This decision level is often called the criterion of the subject.

Now we can get to how hits, misses, false alarms and correct rejections occur.  When the signal is above beta the person will report seeing the signal and be correct with a hit.  If the signal is below beta, the person will report the signal absent an this will be a miss.  If the noise alone is above beta, the person will  report the signal present and make a false alarm.  Finally, when the noise is below beta then the person will make a correct reject.

You can change the values of d' and beta in the table above and you can see what happens to the figure.  Just click on the two cells in red and you can change those values by simply typing in a new value.  Play around and see how d' and beta change the curves and percentages of hits and false alarms.  A good suggestions it to play systematically like you are doing an experiment.  For example, set a value of d' and then observe the hits and misses.  Then systematically change beta to several other values and see how the hits and false alarms change.  Repeat this set of actions for several values in d'.

Where to from here:

More on the Outcomes of STD

The Receiver Operating Characteristic