Is There a Threshold?

Signal Detection Theory makes a very strong statement about the concept of the threshold.  It says that there is no such thing as a threshold.  Let us see why this theory makes this claim.  First recall that the basic concept of threshold says that it is the stimulus intensity where a subject is able to detect a stimulus 50% of the time.  Signal Detection Theory says no such single stimulus intensity exists.

Below is a repetition of one of the earlier figures but it highlights the hits which represents how often a subject detects a stimulus or signal when it is present.  Try these exercises:

  1. Set d' to 0.  Here the stimulus is completely the same as the noise.  It is black on black, silence on silence.  Now move beta around and see if you can find a point where the hits are at or above 50%.  If you can then this stimulus should be above threshold even though it is identical to the lack of a stimulus.

  2. Set d' to a large value, say 7.  Now the curves do not overlap and the stimulus is obviously different from the background.  However, adjust the beta again and see if you can make the hits less than 50%.  If you can then this stimulus, much stronger than the stimulus in 1 above, is below threshold.


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So what is going on here?  From the Signal Detection Theory point of view, there is no single stimulus intensity that leads to detecting the stimulus 50% of the time.  That can be true, according to Signal Detection Theory, for any stimulus intensity.  Signal Detection Theory argues that the concept of the threshold ignores the decision making of the subject that goes on in detecting stimuli.  Thus, there is no threshold.  Signal detection theory argues that d' is the proper measure of sensitivity not threshold.

Where to from here:

The Receiver Operating Characteristic