I could not get a good fit for a Gaussian model of variation in the duration of a behavior. I thus rounded durations to the next integer (nearest minute) and used a Poisson distribution, which worked just fine. Does anyone know if it is correct to round decimals in a [theoretically] continuous variable? If yes, could you please provide references for it? Thanks.
This doesn't seem sensible as the probability model would be incorrect. There are options for continuous outcomes like log transformation, gamma regression, shifted lognormal and so on or even bootstrapping of a robust regression.
Classically people used to use the square root transformation for Poisson data in regression, so it seems plausible if Poisson provides a good fit then the square root or log transform of Y might be OK.
Yes you can.the answer as to why depends on 2 things: first what scientists call significant digits and second on how a digital computer stores numbers. There's millions of references. D. Booth.
There are tons of papers related to the distribution of response times. Their distributions obviously vary by context, but log-normal and Weibull (e.g., http://pcl.missouri.edu/sites/default/files/rouder.psychometrika.2003.pdf). Time is what Mosteller and Tukey (1977) call an "amount" and suggest ln(x + c) where c is a small number (they call it a starting value, but it has several names). The Box-Cox transformation could also be used. What transformations (other than rounding) did you try?
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