Combine Likert Scale with accuracy of responses I am trying to transform my experiment results into variables and I am having some issues.
Data:
One likert scale 1-9 (


*

*1 = " I am sure I havent seen this before”

*5 = "Not sure”

*9 = “I am sure I’ve seen this again”


So, I was measuring the certainty of the response.
However, the response had also a right or wrong answer, which affects the accuracy of the response.
Accuracy is 0 or 1 (0 = false, 1 = correct). Participants who answered 1-4 but actually saw the image before were labeled as wrong, and those 6-9 were labeled as right. The opposite for those images presented only the second time.
(I realised I shouldn’t be using a likert scale for this purpose, as its meant to be for opinions and not right/wrong responses).
Although I could only use the accuracy of response as my dependant variable, I was thinking that I should utilise the certainty as well. I am thinking about transforming my likert scale as :
1 = 4 
2 = 3
3 = 2
4 = 1
5 = 0
6 = 1 
7 = 2 
8 = 3
9 = 4
And accuracy as:
0 = -1
1 = 1
Then multiply both variables to get my final accuracy with certainty, with a range of -4 to 4, using certainty as a weight.
Would this approach be a correct way of dealing with my example ?
 A: Yes, that is OK.
Another option would be to recode answers for images that was actually not seen by participants before. In those cases you can recode 1 to 9, 2 to 8, 3 to 7 and so on (or just take $10-x$, where $x$ is original answer).
This would results in scores 1 to 9 for each question. If you prefer -4 to 4 scale, just subtract 5.
A: This is not really an answer but rather an extensive comment.


*

*What are you after, what is your dependent variable, what is your design?

*You probably have not only correct and incorrect, but rather true positives, true negatives, false positives, and false negatives. This is more informative, and you may use measures such as hit rate, d', ROC curves, etc.

*You loose information by combining accuracy and confidence into one measure. Making a combined model of both measures is much more complicated but will give you more information.

*Cognitive psychologist often have similar data (accuracy + confidence) and use models from signal-detection theory or multinomial processing tree models (e.g., Heck et al., 2018; Erdfelder et al., 2009).

*Confidence rather than certainty might be a better term for googling.
Heck, D. W., Erdfelder, E., & Kieslich, P. J. (2018). Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables. Psychometrika, Advance online publication. doi:10.1007/s11336-018-9622-0.
Erdfelder, E., Auer, T.-S., Hilbig, B. E., Aßfalg, A., Moshagen, M., & Nadarevic, L. (2009). Multinomial processing tree models. Zeitschrift für Psychologie / Journal of Psychology, 217, 108–124. doi:10.1027/0044-3409.217.3.108
