Signal Detection Theory




SDT Outcomes


Is there a Threshold?




This figure is basically the same as the last figure but it highlights the portion of the noise curve that will lead to false alarms or correct rejections and the portion of the signal + noise cure that leads to hits or misses.  Recall that when a the sensory signal strength is stronger than the criterion, the subject will respond that the signal is present regardless of whether the signal is present or not.  So when the noise is greater than criterion the subject responds "present".  That region of the noise curve is highlighted in red below when you click on the Show False Alarms button.  Correct rejections occur the rest of the time that only noise is present and that is indicated by the shaded region in green below when you click on the Show Correct Rejections button.  If this seems odd to you that a person would respond that the signal is present when the signal is not present, you need to realize that the person does not know that the signal is present or not.  All that they know is that there is some activity in that sensory dimension and that a signal might be present.  They have to make a decision as to whether the signal is present or not based on confusing information.

The hits and misses work the same way as the false alarms and correct rejections do but on the signal + noise curve.  Hits will be show as a blue region when you click on the Show Hits button and misses will be shown in purplish color which you click on the Show Misses button. You can manipulate this figure just as you did the last figure so try it out and watch particularly what happens to the hits and false alarms.  This is also a table now that gives exact percentages of time that hits, misses, correct rejections, and false alarms will occur.

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Notice that the hits and misses always at up to 100%.  That is because you will either have a hit or miss when a signal is present.  The same is true for the false alarms and correct rejections.  They make up 100% of the trials when the noise only is present.


The curves are directly related to the percentages in the table.  Let us look closely at the signal + noise curve to see how.  Recall that the height of the curve relates to how likely a certain strength in the sensory pathways will occur.  The higher the curve the more common that strength of nervous system activity will be.  So if you add up all the probabilities under the entire curve it should add up to 1.00 because that indicates all the times that the signal was present.  That is 100% of the time the signal is present.  Thus, we are talking about the area under the signal + noise.  Well, that proportion of the area under the signal + noise curve that is above beta represents the probability that a hit will occur.  Measure that area and divide it by the total area and you have the probability of a hit.  A miss is the area under the signal plus noise curve that is below beta divided by the total area.  These two regions add up to 1.  Thus, it is the size of the region under the signal + noise curve that directly give the percentage of signal trials that will give hits.  The same thing works for false alarms and correct rejects but it uses the noise only curve.

Where to from here:

The Receiver Operating Characteristic

Is there a threshold? Costs and Benefits in SDT