My dependent variable are reaction times (RTs) in a psychological experiment. The experiment features a control condition and an experimental condition and for each subject, I have several hundred realizations of each condition (the variance in this experiment is pretty large, both the intra- and inter-individual). I calculate differences by subtracting the RTs in the experimental condition from those in the control condition and in the mean over trials and subjects, I get a value significantly different from zero.
Now my problem: From a theoretical perspective, I derive the hypothesis that the experimental condition differs only in some of the trials significantly from the control condition and that the differences in the means comes from this proportion, only. In other words, I suspect that the RT from some trials in the experimental condition is drawn from the same distribution as the control trials and only some are from a different distribution. I could possibly come up with a theoretical estimate of the size of this proportion but an approach that would allow to estimate it from the data would be even better.
Is there a way to statistically test this hypothesis against the hypothesis that all experimental trials are from the experimental distribution?
I guess, I can rephrase the problem as follows: Can I test whether the data from the experimental condition is from a bimodal distribution rather than from a unimodal one and, furthermore, is one of the modes identical to the mode of the control-distribution?
thanks a lot,