I know that sensitivity (d') is typically calculated as follows:
d' = z(Hit Rates) - z (False Alarm Rates)
I understand this as the idea is to standardize both distributions, and to then calculate the z-score, which allows to calculate a distance within the same scale so to say.
What is however very confusing to me is the visualization of the process. I am using the following plots from these slides:
My questions are as follows:
(1) As in the plot above, d' is always depicted as the difference of the means of the two distributions (of signal and noise, for instance). Say however that I find in my data that the Hit rate (or Hit probability) is 0.8 - I would think that now, I would need to find z(Hit = 0.8), would this not be to the right of the mean:
Is this correct?
(2) In addition, I am am uncertain about the arrows associated with Z(CR) and Z(H) on panel A above.
For one, in my opinion, CR includes the entire area before the criterion. The arrow, however, associates Z(CR) with only the distance mean-criterion - why?
Then, if Z(X) refers to the cumulative probability density of variable X, Z(X) should be the entire density up to X. In the case of Z(CR) in panel A,however, it seems that it is only the part from the mean of the noise distribution to criterion. So what does then the Z(..) notation mean in this context?