Signal Detection Theory
I promised one but I have three examples for you.
The Classic Radar Operator Example
The signal detection theory evolved out of developments of communications early in this century. One of the situations where the application of this theory to human perception was first noted was in the use of early radar in WWII. This radar was not the nice computer processed fancy color image we are used to on the Weather Channel. Instead, it was a circular disc with a line sweeping around from the center representing the current direction of the radar antenna. Behind this line were briefly illuminated dots. See the figure below for an attempt at a representation of this situation.
These green dots trailing trailing the sweeping are are visible only briefly and can be caused by many different object in the environment or even just the weather itself. The weather operator in WWII, often alone on the southern coast of Great Britain, would have to decide if these dots were enemy aircraft or not.
So we have noise: stray dots on the screen. We have a signal, dots caused by the aircraft of the enemy. We have an ambiguous situation. It was often hard to tell the different between the two sources for the dots on your screen. So the operator has to make a decision about what to do when he sees dots. Are they noise or enemy aircraft? If the operator thinks the dots are aircraft he is to alert the nearest air force base to launch planes to intercept the enemy. The table below puts this situation into a signal detection framework.
With this example it is easier to see some of the effects of different decisions. In this example if the operator makes a:
As you can see, the correct decision is very important. Errors have negative consequences or costs associated with them.