How to check if two results are consistent

I'm looking at an astronomical object. In one observation, it does something (not relevant what :) 2199 times out of a possible 2936.

In another (later) observation, it occurred 2094 times out of a possible 2936.

Is it possible to say anything about whether the object has changed at all, or if the change from 2199 to 2094 is just a statistical thing?

Perhaps I have to find the mean of the two = 2146, then approximate by assuming Poisson stats to say that standard deviation = sqrt(2146) = 46. And then I can say that both of the samples above are within 1 sigma of the mean.

This doesn't seem quite fair thought because you are finding a mean FROM the samples, so of course the mean is going to be quite close to both of them.

I was thinking about using binomial stats to find the variance, but I don't know 'p'.

• What about a 2 sample test for proportions? I.e., comparing the null hypothesis $H_0:p_1 = p_2$ vs. $H_A:p_1\neq p_2$. This of course would depend upon if you can say that the two samples you looked at are independent, which in your case doesn't sound like the case. – RustyStatistician Feb 12 '16 at 23:42
• Actually you can use McNemars test for dependent proportions. Here is something similar: stats.stackexchange.com/questions/34430/… – RustyStatistician Feb 12 '16 at 23:48
• @RustyStatistician the user hasn't necessarily claimed the experiments were paired. – AdamO Feb 13 '16 at 0:02
• @AdamO my apologies. I didn't realize McNemars test was for paired samples. – RustyStatistician Feb 13 '16 at 0:12
• You say Poisson stats, but shouldn't this be a binomial stats case? – jwimberley Jan 3 '17 at 1:44