Question

6) Performance data collected during a working day for two operators working on different luggage scanners at an airport is presented in the following tables Operator 1 Response Signal (Weapon) Noise (No Weapon) Yes Weapon No Weapon 1800 200 1500 500 Operator 2 Response Signal (Weapon) Noise (No Weapon) Yes Weapon No Weapon 600 1400 60 1940 Using signal detection theory, calculate the criterion value (Yc) and Discriminability index (d') for each operator (12.5 points) Based on the relationship between Yc and d', classify the operators (2.5 points)

Answer 1

Here data of Operator 1 and 2 is as

Operator 1	Signal
	Present	Absent
Yes	1800	1500
No	200	500
	p(Hit)= 1800/3300 = 0.55	p(FA)= 1-0.55 = 0.45
	z(Hit)= z(0.55) = 0.13	z(FA)= z(0.45) = -0.12

Discriminant index = d' = z(Hit) - z(FA) = 0.13 + 0.12 = 0.25

and Criterion Value = Yc = -[z(Hit) + z(FA)] / 2 = -(0.13-0.12)/2 = -0.01/2 = -0.005

Similarly

Operator 2	Signal
	Present	Absent
Yes	600	60
No	1400	1940
	p(Hit)= 600/660 = 0.91	p(FA)= 1-0.91 = 0.09
	z(Hit)= z(0.91) = 1.34	z(FA)= z(0.09) = -3.13

Discriminant index = d' = z(Hit) - z(FA) = 1.34 + 3.13 = 4.47

and Criterion Value = Yc = -[z(Hit) + z(FA)] / 2 = -(1.34 - 3.13)/2 = 1.79/2 = 0.895

Here based on relationship between Yc and d' we classify the operators as

For operator 1st Yc = -0.005 so Here the observer is said to be ‘unbiassed’ in favour of ‘yes’ responses.

And For operator 2nd Yc = 0.895 so Here the observer is said to be ‘unbiassed’ in favour of ‘No’ responses.