Signal Detection Theory

Topics

Introduction

Basics

SDT Outcomes

ROC

Is there a Threshold?

Quiz

Costs and Benefits in SDT

One question that I have danced around so far is what determines the criterion a person will set.  Since the criterion is under the subjects control, it is possible that a person can set their criterion in a capricious or random manner.  However, it is usually thought that the person sets the beta to maximize or near maximize the outcome of this ambiguous or confusing situation.  Recall the example.  There are costs associate with mistakes as well as benefits or positive outcomes with correct decisions.  It is expected that in many cases the subject tries to maximize the total outcome which is the benefits subtracting the costs.  While people can differentially value many benefits and many costs money has a fairly precise value and can allow a clear way of seeing how costs and benefits can alter the subjects beta.

The figure and table below can illustrate this situation.  You can change both the d' and the criterion as before.  In addition there are three new elements to the table:

1. A cost/benefit matrix.  Here you can manipulate how much a hit or a correct rejection are worth and how much a false alarm or miss cost in cents.

2. An average outcome matrix.  This reports on the average of 100 trials what the money made or lost for each of the outcomes would be on average.  This is simple the percentage for each outcome multiplied by the cost or benefit.

3. The total.  This is the overall outcome, on average, for this 100 hypothetical trials.  This value is the overall expected outcome for this situation.

Try this out, set up a cost benefit situation and a d' and see what criterion leads to the greatest gain, or least loss.  Then change the costs and benefits and see what that does to the criterion that leads to the best outcome.  To simplify your task you can set misses and correct rejections to 0 and change only hits and false alarms.  Remember, only put 0 or positive numbers for hits and correct rejections.  You should put only 0 and negative numbers in for false alarms and misses.  See what situations lead strict criterions and what situations lead to lax criterions.  For each d' plot the ROC curve using the hit rate and false alarm rate that gives the most positive outcome for several different betas and compare it to the ROC curve for the same d' on the ROC curve page.

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