## d'prime for rating design

I am doing individual differences in sound perception where I ask the participants to listen to a pair of sound and judge whether they are the same or different.

The answer choice and scoring are as below:
(number) is the score

Definitely Same (1) Probably Same (0.5) I Don't Know (0) Probably Different (0) Definitely Different (0)

Definitely Same (0) Probably Same (0) I Don't Know (0) Probably Different (0.5) Definitely Different (1)

I then convert the score to the standard d', z(h)-z(f). Therefore the d' coefficient is their "score".

Can someone tell me whether this is the right way to do?

I have been told the best measure of sensitivity is the area under the ROC (Ag). But I don't understand how is this applicable to this design if I want to calculate sensitivity index for each person.

(Detection Theory Book, p.64)

Ag= 1/2 {SUM symbol} (Fi+1 + Fi) (Hi+1 + Hi).

The index i tracks the ROC points so that (F1, H1) equals (0,0), (F2, H2) is the first point to the right, and the last point is (1, 1).

Can someone correct me what I have done wrong or how to calculate based on A(g) formula (i.e. what is Fi+1)

Thanks.