Question

7) Following table represents the performance data of an operator for two signal detection tasks. Calculate the criterion value (Yc) and Discriminability index (d') (12.5 points) Compare the difficulty level the tasks (2.5 points) Task 1 Response Signal Noise Yes Signal 475 30 Yes Noise 25 470 Task 2 Response Signal Noise Yes Signal 305 200 Yes Noise 195 300

Answer 1

Here we calculate Criterion value (Yc) and Discriminant Index (d') for two different signal detection task as

Task 1	Signal
	Present	Absent
Yes	475	30
No	25	470
	p(Hit) = 475/505 = 0.94	p(FA) = 1-0.94 = 0.06
	z(Hit) = z(0.94) = 1.56	z(FA) = z(0.06) = -3.26

Let,

Discriminat Value = d' = z(HIt) - z(FA) = 1.56 + 3.26 = 4.82

And Criterion Value = Yc = -[z(Hit) + z(FA)] / 2 = -[1.56 - 3.26] / 2 = 1.7/2 = 0.85 ....................... (1)

Similarly

Task 2	Signal
	Present	Absent
Yes	305	200
No	195	300
	p(Hit) = 305/505 = 0.6	p(FA) = 1-0.6 = 0.4
	z(Hit) = z(0.6) = 0.26	z(FA) = z(0.4) = -0.26

Let,

Discriminat Value = d' = z(HIt) - z(FA) = 0.26 + 0.26 = 0.52

And Criterion Value = Yc = -[z(Hit) + z(FA)] / 2 = -[0.26 - 0.26] / 2 = 0 ............................ (2)

From equation (1) and (2) we conclude that,

When C=0 the criterion is midway between the S and N distributions. Here the task 2 is said to be ‘unbiassed’.

And When C > 0 The task 1st is biased in favour of ‘No’ responses.