I have a situation where I measure something for a long time, and occasionally a seperate event of interest will occur. I want to determine if these events have a significant effect on the signal I am measuring. So I am thinking of taking the signal value at each event time, and comparing it to times when there was no event.
But as I see it there are a couple of ways to do this. First, I could take the whole population mean over all the data I have collected (ignoring presence or absence of an event), then do a 1-sample t-test on the event present data set against the whole data mean. Or I could take the mean over all the data, but excluding the times the event happens but still do a 1-sample test against the measured no-event mean.
Or I could take my set of event responses and create a surrogate 'no-event' data set of the same size from points chosen at random when there was no event and do a 2-sample t-test between these two. This surrogate set could have the same number of points as the event set, or could have many more (I have much more no-event data than event data).
So I am in a bit of a muddle as to which of these would be the best in terms of statistical power and avoiding any mistakes. Any advice is appreciated. I would especially be interested in understanding conceptually the reason for any preference of one method over another.