I plan to collect data from 2 groups of people (Gp_1 and Gp_2), some few hundred people in all. Each person will respond to 100 yes/no tasks, each response yielding both accuracy and reaction time data. Each person will respond to two types of stimuli (Stim_1 and Stim_2), 50 yes/no tasks for each type of stimulus.
I would like to compare the groups on both accuracy and reaction time. My primary research hypothesis is that Gp_1 will respond more accurately than Gp_2 to Stim_2. A secondary research hypothesis that there will be no between group difference in accuracy for Stim_1. I do not have a prediction as to the reaction times of the two groups to the two stimuli (neither for means or for variance).
I plan to compute the mean accuracy and mean reaction time for each person to the two types of stimuli. After that, there seem to be at least two options: (1) get difference scores for each person for accuracy and for time to respond for the two types of stimuli, or (2) form a ratio for each person for accuracy and for time to respond for each of the two types of stimuli. Perhaps there are other options. I plan to conduct statistical tests.
How might the power of the two data analysis approaches compare? Or what conditions should I consider to compare power?
Should I expect one of the two statistics above to better conform to the assumptions of a parametric test of statistical significance?
Are there other approaches I should be considering for comparing the two groups on their performance on the two types of stimuli?
This question is similar, but has no answer: Ratio measure vs. difference measure?