# When to use B'' or B''D as a measure of response bias?

I hope this is not a stupid question, but here it goes:

Based on information from Macmillan and Creelman's Detection Theory (2005) and Pallier's R-code that I found here, Computing discriminability and bias with the R software, I came up with code to calculate $B^{''}$ (used as a measure of response bias in psychological "yes/no"-experiments). Pallier suggests a diferent measure of bias than Macmillan & Creelman (pp. 100-104, 371).

In the code below, "fa" stands for false alarm rate and "hit" for hit rate.

> bpp <- function(hit, fa) {
a <- ((hit*(1-hit)-fa*(1-fa)) / (hit*(1-hit)+fa*(1-fa)))
b <- ((fa*(1-fa)-hit*(1-hit)) / (hit*(1-hit)+fa*(1-fa)))
a[fa>hit] <- b[fa>hit]
a[fa==hit] <- 0
a
}


Here is the original $B^{''}_D$ code as provided by Pallier:

> bppd <- function(hit,fa) {
((1-hit)*(1-fa)-hit*fa) / ((1-hit)*(1-fa)+hit*fa)
}


What is the difference between these two measures of response bias? When is it appropriate to use which?

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I am taking no answers as a sing that I am totally on the wrong track here? Or is the question just too... well, stupid? –  kat Jul 12 '12 at 9:58
Do you have access to the paper referenced by C. Pallier, Measuring recognition memory? –  chl Jul 13 '12 at 9:11
@chl: Yes, I do, if needed, I could forward it by mail... –  kat Jul 13 '12 at 14:01
I have it too. I though you were asking (in part) about the rationale for using $B^{''}_D$ which looks to be detailed p. 276 of the article. –  chl Jul 13 '12 at 14:28
Yes, you got that right. But I simply don't understand the explanation given there. Is there a way to explain this to someone who does not have such a firm grasp on maths? ... –  kat Jul 13 '12 at 15:25
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## 1 Answer

Handbook of Human Factors and Ergonomics by Gavriel Salvendy, p. 973-974, cites some other works that recommend to use BppD = Donaldson's one (cited by Pallier). The other code you mention comes from Grier. Hope it helps.

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