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Consider the following situation: You are driving down the road, and you think you heard a sound that might have come from the engine. Say it sounded kind of like a clunk. Now, you have your stereo going, and there are sounds from the road, so you are not sure. If you car is relatively new and has a history of smooth running, perhaps you will decide that you didn’t really hear anything. Your hearing is “playing tricks” on you. Perhaps instead of the fine automobile described above you are driving an old car that has a history of spending nearly as much time in the shop as on the road. In this case, you might decide that you did hear something and head to the nearest service center. What is important in this example is that even in this very basic sensory discrimination, there is a cognitive decision-making element that needs to be taken into account.

Signal detection theory attempts to understand the role that decision making plays in these situations. Examine the situation above a little more carefully. All the possible outcomes are shown in Table 1(a). In the real world, the stimulus event does not always occur. So it is possible that the clunk either occurred or did not. These two possible stimulus events are indicated across the top of the table. In either case, and to some extent independently, of whether the clunk happened or not, you can decide that you heard the clunk or not. These possible judgments on your part are shown on the left-hand side of the table. The four cells of the table are the possible outcomes. For example, the clunk could have happened, and you could decide that you heard the clunk and so you go get the car serviced. That outcome is in the upper left hand cell of the table. Thus, two of the outcomes, deciding the sound occurred when it did and deciding the sound did not occur when it did not, are correct responses and have positive outcomes; the other two outcomes represent incorrect decisions and have negative outcomes. It is, of course, in your best interest to maximize the positive outcomes while minimizing the negative outcomes.

Table 1(a)
Signal Detection Theory Possible Situations

The Clunk:
Happened Did not Happen
You Decide That
the Clunk:
Happened You get
needed service
You pay an
unneeded service visit
Did not
You break down
on the road
You go happily
on your way
Table 1(b)
Signal Detection Theory Possible Situations
The Signal Is:
Present Not Present
You Decide
That the
Happened Hit False alarm
Did not
Miss Correct rejection

Table 1(b) gives the general terms to what has been described. The clunk in our original example is now called the signal. The signal is simply what we have been calling the stimulus. It is the event in the world that a person is trying to detect. If the signal is present and you judge it happened, it is a hit; if the signal is present but you judge it did not happen, it is a miss; if the signal is absent and you judge it happened, it is a false alarm; finally, if the signal is absent and you judge it did not happen, it is a correct rejection.

So let’s look at a model of signal detection, starting with a visual detection example. Signal detection assumes that there is “noise” in any system. In this example, if we have an old car, we may hear clunks even when the car is operating effectively, or even tinnitus in our ear, or something rustling in the trunk. The signal is what you are trying to detect. In our example, it is a clunk that means the engine is in trouble.

See the illustration to see how Signal Detect Theory describes this situation.


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To see the illustration in full screen, which is recommended, press the Full Screen button, which appears at the top of the page.

Illustration Tab


Below is a list of the ways that you can alter the model. The settings include the following:

Noise: check to display the Noise curve. This curve represents how likely a given stimulus intensity will occur when there is no signal (stimulus) present.
Signal+Noise: check to see the Signal+Noise curve. The noise does not go away, but the stimulus adds to the noise, making the Signal+Noise curve move to the right of the Noise curve. This curve represents how likely a given stimulus intensity will occur when the signal (stimulus) is preseent.
Sensitivity-d': the difference in the position of the Noise and Signal+Noise curve relates to how easy it is to detect that the signal is present. The greater the difference, the easier the detection. We call this difference sensitivity and measure it with the measure called d' (pronounced d prime).
Show Overlap: click to highlight the region where the Noise and Signal+Noise curves overlap. Where there is overlap, a given stimulus intensity could be by either the noise alone or by the signal. You cannot know for certain. As you increase d', the overlap gets smaller.
Show d': click to add a visual representation of d'. An orange line will connect the two peaks. The larger the d', the longer the line.
Sample: collect the number of dots to form a histogram, showing the number of dots at each sensory intensity that has been collected. A vertical line will be displayed on the graph to show the current number of dots. The color of the histogram and dots match the color of the noise of sample+noise distribution that is being sampled from.
Sample From: is the sample from the Noise only or the Sample+Noise distribution, that is, is there no stimulus (Noise) or there is (Signal+Noise). The number of dots will be determined by the selected distribution.


Pressing this button restores the settings to their default values.