Me is not sure on bias calculation. My suggest to you is to use discriminant analysis and to create the spaces for yours two tasks< from the beginning. As a result you will receive the significant/non-significant differences. All the best.

As I understand, subjects have to discriminate blue from red items in the encoding phase. So, you may define "red" as signal and "blue" as noise (or voce versa). False alarms are answers with "red" with blue stimuli given.

However, in my view, it is sufficient if you calculate correct answers and false alarms in the recognition phase. "Old" answers with old stimuli are hits, "Old" answers with new stimuli are false alarms. I would declare the encoding phase as "training phase".

All the best, Hede

Dear Hede, the bias assessment is nothing (frankly). You have to investigate the discrimination between yours two pools of the data. Moreover, you could also use the multifactorial regression analysis/models where all yours variables will be the predictors, and "red-blue" are crucial. Good luck. All the best, KL

Dear Konstantin,

sorry, I can't accept your answer. The question addressed the calcuklation of respond

se bias and not the calculation of sensitivity. All the best, Hede

Be happy: Do not worry. I proposed to you the approach. Up to you. Good luck. K

There is a formula to calculate response bias as follows:

beta = P(X|S) / P(X|N)

Hope this helps.

https://en.wikipedia.org/wiki/Response_bias

http://psych.colorado.edu/~lharvey/P4165/P4165_2003_1_Spring/2003_Spring_pdf/P4165_SDT.pdf

https://www.google.com.ua/?gws_rd=ssl#q=response+bias+calculation

Did you try to use Internet? Again, there are other approaches

I would suggest looking at some literature in signal detection theory/recognition memory. The following book is a good review (Macmillan, N., & Creelman, C. D. (2005). Detection theory: A User's Guide (2nd ed.). Mahwah. NJ: Lawrence Erlbaum Assoc Inc.)

If your new, previously seen red, and previously seen blue shapes were randomly intermixed at test, and presented in black, you can only calculate one false alarm rate across the two classes of items (red and blue). You can calculate differences in accuracy just by looking at the hit rates for red and blue items as others have mentioned. You can also look at discrimination measures like d' (z(hits)-z(false alarms)) but your false alarm rates would be the same across both item types so the difference would be in the hit rates anyways. 

Importantly, you can't calculate a meaningful response bias measure across the two classes of items, since you only have one False Alarm rate. In this case adopting different response biases would require participants to remember what color the item was at study, at which point they already know the item was a target. That is, if I were to adopt a different response bias for red and blue items in this task, I would have to remember whether the current black item I was judging was red or blue, and if I remember it was red, then I already know the answer is 'old' and that I studied it. 

There are several papers that have looked at response bias using memory strength manipulations, which can help give you an idea of how to set up a study if you would like to consider two separate false alarm rates for each class of your items. I cite some examples below: 

Verde, M. F., & Rotello, C. M. (2007). Memory strength and the decision process in recognition memory. Memory & Cognition, 35(2), 254–262. http://doi.org/10.3758/BF03193446

Stretch, V., & Wixted, J. T. (1998). On the difference between strength-based and frequency-based mirror effects in recognition memory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 24(6), 1379–1396. http://doi.org/10.1037/0278-7393.24.6.1379

However, for your current data it makes sense to only look at accuracy using the same false alarm rate across both red and green items, or alternatively just compare the hit rates to see if there was a difference. 

Compute "hit rate" (P(yes|old) and "false alarm rate" (P(yes|new), then use the table in my Psych. Bulletin article (Hochhaus, L. (1972). A table for the calculation of d' and B. Psychological Bulletin, 77, 375-376.) to find d' (sensitivity) and B (response bias) for each participant.