Short Notes on Theory of Signal Detection Walter Schneider

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Presentation transcript:

Short Notes on Theory of Signal Detection Walter Schneider Links calculator http://wise.cgu.edu/sdtmod/index.asp handout http://www.cns.nyu.edu/~david/handouts/sdt/sdt.html

Normal Distribution

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.

Criterion Shift

d’ and ROC

Basic Curves

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

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

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)

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)