# Signal Detection Theory

### Topics

Introduction

Basics

STD Outcomes

ROC

Is there a Threshold?

Quiz

# var sc_project=6064335; var sc_invisible=1; var sc_security="bc1c3a15"; Basics

The figure below illustrates how signal detection theory conceives of what is going on inside of the sensory or 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 of the same intensity.  There are random variations in the intensity of the nervous system even when nothing is there.  This aspect of our functioning is indicated by the green curve labeled "Noise".  The theoretical shape that describes how likely any given level of activity in our nervous system occurs is our old friend the normal or bell-shaped curve.  The noise curve in the grave has a mean strength for the noise and a standard deviation given in arbitrary values below.  The peak of the curve is over the level of activity that is most likely to occur.  Levels of activity above or below the mean get progressively less likely as indicated by the curve moving towards the 0 level.  This situation is the mess or noise that confuses the detection of a weak signal.  When the signal is present, the noise curve moves to the right on the graph because the signals adds a constant value on to the noise.  Press the Show Signal button below to see the "Signal + Noise" curve.  This situation is indicated by the orange curve below.  It is called the Signal + Noise curve because the noise does not go away.  The signal is added to the effects of the noise.  The Signal + Noise is also a normal curve with the same standard deviation and the Noise.  The Signal + Noise curve is just the Noise moved to the right by the presence of the signal.  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, they overlap a great deal which means that many sensory signal strengths could be caused by either the noise alone or the signal plus the noise.  Press the Show Overlap button to highlight the range of sensory response levels that could be either signal or noise.  As a person you only know the sensory signal strength, not what caused the sensory signal strength.  It is the presence of the overlap that causes the detection of weak signals can be difficult.  How difficult is indicated by a measure called d' (pronounced d-prime).  The larger the d' value, 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.  You can show the d' for the two curves by clicking on the Show d' button.  A blue line will connect the peaks of the two curves which indicates the distance that is being measured to get d'.  You can also adjust d' using the slider below the figure.  As d' increases, the amount of overlap decreases.

The other thing to notice is the value called Criterion.  Press the Show Criterion button to show a vertical yellow line that will indicate where the criterion is.  The criterion is a cutoff value determined by the person trying to detect the signal.  If the sensory signal strength is stronger than the criterion value, then the person will report the signal as present.  If the sensory signal strength is less than the criterion, the person will report the signal as absent.

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

You can change the values of d' and criterion using the sliders below the graph and you can see what happens to the figure.  Play around and see how d' and criterion change the curves and proportion of the noise alone curve and the signal + noise curve falls above or below .  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 criterion to several other values and see how the hits and false alarms change.  Repeat this set of actions for several values in d'.

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