If you found the constant then you could subtract it from every measurement and make a confidence interval for the mean. Since you can change your time intervals to 1 minute it should be very easy to find the constant if you are only monitoring 10 houses.That was bad news I think! If I find the constant, then I could subtract it and then do the Pearson X^2 ?
On a Poisson, What is over-dispersion really comming from, finding more high values weighting the tail than for the polulation? I feel it would be the opposite. or is it due to noise that squared get higher weight since that is usually not Zero centered ?