I have a set of univariate data, where the response variable in a trial is a sequence of time intervals between button presses (my experimental subjs have to press a button intermittently to react to some task conditions). Eventually I have to run a within-subject regression to see if my hypothesized predictors are indeed significant. However, the first thing I want to do is to show that the subjects didn't just press the button randomly. In other words, I need to make sure that the person didn't just press a button at a regular pace, (averaged response times + random variability).
One idea I have is to check if my data resemble a Poisson process, in which arrival times occur randomly at a certain rate. Based on what I've looked up on using Poisson process so far, there are two approaches to fit the poisson process to my time interval data:
1) count how many times the person pressed a button in each trial of fixed time period. Then I can follow the Poisson distribution fitting process to count data.
2) the wait times between events in a poisson process is said to follow an exponential distribution. So I can try to fit "exponential" distribution to the time intervals. In that case, should I try to fit a bunch of different distributions such as Exponential, Gamma, and Weibull?
In either case, I would then use a chi-square goodness of fit test and/or a QQ-plot to assess whether the distribution fit can be rejected.
Any advice would be greatly appreciated. Is fitting to Poisson Process to my data even the right way to go? I would be happy to hear about any other suggestions. Thanks in advance.