But if your goal is to keep your good shoes dry at all costs, being accurate about whether it's going to rain or not by having the unbiased threshold doesn't matter. The unbiased threshold is the point at the middle of your d' where the curves intersect it is also the point of maximum accuracy. You have a response bias from a threshold that is statistically either higher or lower than exactly in the middle of your d'. Notice that biasing your responses can be completely reasonable (it seldom rains here). If you live in LA like I do, you might be biased to say no - that there is no signal (rain) - for even medium-high levels of evidence because LA is in a drought. Response bias is your tendency to say yes or no to different levels of evidence, or where you put your threshold. d' is the distance from the peak of the noise distribution to the peak of the signal distribution. Our ability to distinguish the signal (such as rain) from noise is what we call sensitivity and we measure sensitivity with d' ("d-prime"). When the signal is absent, external and internal noise fully explain whatever level of evidence we have, which is why we call this case noise. Environmental distractions, external noise, could be someone walking by or a flickering light or a change in room temperature. Distractions in us, called internal noise, are things like feeling hungry or spacing out or blinking.
![signal detection theory signal detection theory](http://gru.stanford.edu/lib/exe/fetch.php/tutorials/nobias.png)
There are always potential distractions in us and in the environment that prevent us from perfectly or even consistently taking in stimuli. If the level of evidence for rain was high enough to be above threshold leading to the prediction of rain, but it didn't rain, we call this a false alarm.Įach of the world states is statistically represented by a normal distribution because perception is probabilistic. The name c orrect rejection tells us that the level of evidence led to the correct decision: low evidence, such as for rain, correctly predicted the world state, such as not raining. Our other two outcomes add up to 100% of times when there is no signal. Together, hits and misses make up 100% of times when the signal is present. If it rains, but the forecast wasn't rain, then we call that a miss - when the signal is present, but the level of evidence was below threshold. This is a hit - when the world state is that the signal (rain) is present, and the level of evidence was above the threshold, high enough that the forecast was rain. Continuing with our rain example, sometimes weather forecasters will correctly predict rain. Threshold, also called criterion and decision boundary, is the level of evidence above which you (consciously or unconsciously) think that the signal is present and below which you think the signal is absent.Ĭrossing the two situation dimensions, world state and evidence, yields four possible outcomes: hit, miss, false alarm, and correct rejection. In other signal detection situations, you might occasionally find out what the world state is - if you keys are where you thought - but not always. In psychology, the evidence dimension - the only dimension you have direct access to - can be sensory or perceptual evidence, memory, etc., such as how clearly and how accurately you remember what you did with your keys. With weather, you definitely can find out the world state. So they use their evidence to make their best predictions, setting some threshold above which they predict rain and below which they don't. We call when the stimulus is present (here, rain) the signal and when it's absent (here, no rain) noise - notice that signal and noise are mutually exclusive categories.īut when forecasters are predicting the weather, all they have access to is various evidence (barometric pressure, humidity, etc.) about what the weather might be later. Take weather forecasts as an example: if the forecast is that it will rain at 4pm (not here in LA, but somewhere), when it gets to 4pm it will be either 100% raining or 100% not, one of two mutually-exclusive world states. Under basic signal detection theory (SDT) there are two situation dimensions, world state and your level of evidence. Signal detection is a theory, research method, and statistical method for explaining and measuring how we act under uncertainty. Sometimes how we respond is biased - like assuming every sound or vibration is the phone when you're waiting for an interview or job offer.
![signal detection theory signal detection theory](http://www.kerrywong.com/blog/wp-content/uploads/2011/01/2000px-Sonar_Principle_EN.svg_.png)
Sometimes we're right, and sometimes we're wrong. We all experience uncertainty: How did I do on that test? What do they think of me? Where did I leave my keys? Is my phone ringing? In these and other uncertain situations, we have to take the evidence we have and make our best guess about the answer.