1. Short Notes on Theory of Signal Detection Walter Schneider
Links
calculator
handout

2. Normal Distribution

3. Hit/Miss & Criterion Turor No Tumor Say “Tumor” Hit False Alarm
Turor
No Tumor
Say “Tumor”
Hit
False Alarm
Say “No Turmor"
Miss
Correct Rejection
Turor
No Tumor
Say “Tumor” 40 5
Say “No Turmor" 10 45
TOTAL 50
The hit rate is 40/50 or as a proportion .80.
The false alarm rate is 5/50 or .10.

4. Criterion Shift

5. d’ and ROC

6. Basic Curves

7. d’ - Sensitivity The formula for d' is:
d’ = z(p(False Alarms))- z(p(Hits))
where z (H) and z (FA) represent the transformation of the hit and false alarm rates to z-scores.
Example
False Alarms = 0.10, Hits = 0.70,
d’= Z (0.10) – Z (0.70) = [1.28] – [-0.52] = 1.8

8. Beta - Criterion Criterion bias ordinate of hit/ ordinate FA
The formula for d' is:
Beta = [Ordinate p(Hit) ] / [Ordinate p(FalseAlarm) ]
Example False Alarms = 0.10, Hits = 0.70,
Beta = [Ordinate (0.70) ] / [Ordinate (0.10) ]
= [0.349] / [0.176] = 1.98

9. Example of Mean 3 subjects
d’ = z(p(False Alarms))- z(p(Hits))
Beta = [Ordinate p(Hit) ] / [Ordinate p(FalseAlarm) ]
Note d’ and Beta must be calculated for each run of an expected sensitivity and criterion separately
Excel Hints
Z(Hit)=NORMINV(Hit,0,1)
Ordinate(Hit) = =1/SQRT((2*PI()))*EXP(-POWER(Hit,2)/2)

10. Practical Considerations
Need significant FAs and misses (>10%)
(NOTE A’ less sensitive to low FAs)
Data must be done with consistent bias and sensitivity
Calculations must be done within subject and if need be within run
To determine average d’ and beta calculate the individual estimates (DO NOT AVERAGE THE RAW HITS AND FALSE ALARMS)