Which is a better statistical option to compare differences across groups? I have two groups (13 experimental and 13 control participants) performing on two cognitive tasks. I have accuracy (omissions, commissions) and reaction time measurement from each test for each person. To avoid type-I error, I was suggested to decrease my number of DVs, I now have d-prime (d') and reaction time (RT) as the DVs (both continuous). I would like to compare performances on both the tasks, across both the groups. My questions pertaining to this design are:


Is d-prime a good measurement to substitute accuracy scores ? or
could you please suggest a unitary index that would reflect
behavioral performance (from omissions, commissions, RT data)
Should I do a one way MANOVA? (IV- groups; DV- test1 d', test2 d', test1 RT, test2 RT)?
or Should I do a mixed model MANOVA? (if yes, how to do this, what are my DVs)?
If you have single-trial data, the drift-diffusion model/DDM and related models, originating with Roger Ratcliff (1976/1978), can simultaneously fit the whole response distribution, both RTs and accuracies. It captures phenomena such that in some experiments, errors are systematically faster or slower than correct responses.

Fitting and interpreting the DDM can be non-trivial, but it has many advantages, such as


accurately accounting for the distribution of RT data
directly relating to cognitive processes (e.g. evidence accumulation speed, sensory encoding speed)


The DDM works by modeling the decision process as a random walk next to (usually two) decision thresholds (e.g. corresponding to the correct and the incorrect button in a 2-alternative false choice task), which after an initial period of encoding begins drifting towards the correct boundary at a speed corresponding to the effectivity of taking up evidence. Occasionally, the drift process reaches the wrong boundary. When a boundary is crossed, execution of the corresponding response is initiated.

The DDM is fitted to the whole RT distribution and the resulting parameters can be submitted to statistical tests between conditions. For an example of hierarchical Bayesian estimation of the model, consider HDDM.

References

Ratcliff, R. &amp; Murdock, B. B., Jr. (1976). Retrieval processes in recognition memory. Psychological Review, 83, 190-214.
Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85, 59-108.
Forstmann, B. U., Ratcliff, R., &amp; Wagenmakers, E.-J. (2016). Sequential sampling models in cognitive neuroscience: Advantages, applications, and extensions. Annual Review of Psychology, 67, 641-666.
Ratcliff, R., Smith, P.L., Brown, S.D., &amp; McKoon, G. (2016). Diffusion decision model: Current issues and history. Trends in Cognitive Science, 20, 260-281.
Wiecki TV, Sofer I and Frank MJ (2013). HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python. Front. Neuroinform. 7:14. doi: 10.3389/fninf.2013.00014