Signal Detection Theory - ARMS (neuropsychology)

What determines whether the patient is diagnosed?

• Performance on test
• Criterion for deficit

Sensitivity: how far are these curves apart? How good can. the participant discriminate between these two curves?

There is also a criterion:

Everything > the criterion: we say that the signal is present.

Everything < the criterion: the signal is not present.

This can also be presented as:

From the data from an experiment you could tell how many hits, false alarms, misses and correct rejections there were; you make the decision matrix.

To calculate sensitivity, you only need hits and false alarms. You can calculate this in excel using:

Hits: =IF(AND(CEL=1,CEL=1),1,0)

False alarm: =IF(AND(CEL=0,CEL=1),1,0)

Then you calculate the sum of hits and false alarms, and then you can fill in the matrix.

Amount of misses: (Total amount of stimuli-present trials) - hits

Amount of correct rejections: (Total amount of stimuli-non-present trials) - false alarms

From your raw data, your matrix might look like this:                                                 

For the decision matrix, you divide everything by the total number:

To calculate sensitivity, we use d’ (d-prime). d’ = how many standard deviations are the mean of the signal and the mean of the noise apart? d’ = 1 stdev, d’ = 2 stdev etc. The smaller the d’, the lower the sensitivity. We calculate this using:

Reasoning: the difference between the means = the difference between the distance to criterium.

To calculate the Z in excel: normsinv(proportion hits or false alarms). So the total formula to calculate d’: normsinv(hits) – normsinv(false alarms). You use the rates for this formula, not the amounts.

You get a negative d’ if the person was worse than 50% chance of getting it right; they can do this purposefully or maybe they didn’t read the instructions well. This person is still sensitive

In summary, the steps for computing d’:

Every person has a criterion. The criterion can change by e.g. change in the instructions to the participant.

There are two measures for criterion: C=criterion, beta=bias.

You calculate criterion using:

If the criterion is 0, the person has no bias to right or left: it’s placed in the middle of the two curves.

Negative criterion: tendency to say  ‘yes, there is a target’

Positive criterion: tendency to say ‘no’

You calculate beta using:

Beta < 1 : tendency to say yes

Beta = 1 : no bias

Beta > 1 : tendency to say no

d’ and the criterion are independent.

With the ROC-curve you combine the d’ and criterion:

This person is just guessing.

There are two assumptions for computing d’ and C:

• Normal distribution
• Equal variances

This is violated whwn the sensitivity (d’) and the criterium are not independent:  the d’ differs for different criteria.

Examples of causes for violation:

• Distribution of noise differs when signal is present
• Smaller chance for signal or noise to occur

Consequences of violation:

• The d’ changes with criterion
• We can still make a ROC, but we can’t compute an average d’ across criteria

You can still calculate the AUC/A’; the area under the curve.

How to check? Look at the ROC curve for multiple criteria:

How to calculate AUC? You can use excel for this:

First rank the proportions! Highest numbers on top.

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