I ran an experiment where I expected that reaction times in two different conditions would differ, and I estimated that one condition would always be associated with longer reaction times.
After collecting the data, I realised that there did appear to be systematic differences between the two conditions, but that individual differences (between participants) seemed to dictate the direction of the difference (i.e., some people responded systematically slower in one condition, and other people vice versa). I mostly just care that differentiation is happening, not so much whether reaction times are shorter or longer in one condition or the other.
What I would like to do is calculate the relative distinction (in reaction times) between conditions. I don't want to use the absolute or unsigned difference in milliseconds, given that different participants will have different reaction time speeds in general.
In my manuscript, I ended up dividing the mean reaction time of condition A by the mean reaction time of condition B, and then used the unsigned difference between that ratio and 1 as the new dependent variable:
the absolute value of 1 - [condition A/condition B]
I received back reviewer comments and they didn't feel I named or communicated this term very well. I said "ratio difference" but I can see why that would be confusing. So I need a standard term, or a more concise and clever definition than I can come up with. Is there a commonly accepted statistical term I have missed?
The other criticism was a lack of significance testing. How can I establish, for each participant, that this ratio is significant, before adopting it as a dependent variable? For each condition (A or B), for each participant, for each block, I have at minimum 30 reaction times. So perhaps I could test, within each block and participant, between the two conditions, as is suggested by this answer. In that case, should I use the test statistic as a DV, or simply report it as validation for using the ratio difference? And I presumably would then correct each participant test's p-value for multiple comparisons.
Edited to add that I have been looking at questions already posted here concerning the use of ratios in regression, but it seems that this is an issue where the ratio is constituted by an interaction, especially if the ratio is meant to be interpreted as a predictor. What I am chiefly concerned with is how unequal the two conditions are, if that makes sense--not necessarily the relative contribution of one factor over the other.
Edited again to add: for anyone else reading this question with a similar issue, these previous questions do a much better job articulating what my original research goal was:
Extracting slopes for cases from a mixed effects model (lme4)
Test whether random slopes are significantly different from 0 for individual subjects