# Comparing the variance of two samples with differing measurement error

1. Jul 24, 2014

### Astr0fiend

1. The problem statement, all variables and given/known data

This is a statistics as applied to astronomy problem. My stats knowledge is horrible. Anyway, the problem:

For several hundred objects, I have a number of different properties for which I have a measurement & associated measurement error. For example, flux density and its associated error. There is a quantity that has been measured for each source that I need to work with (as explained below), that I'll call 'y'. The variance in 'y' consists of two contributions: Measurement error, which is known with a high degree of precision, and an underlying variation that is a property of the sources themselves, which I'll refer to as the 'intrinsic' contribution.

From the underlying population, I have drawn two samples based on whether or not an object meets some criteria -- the details of this particular criteria are unimportant. I want to compare the variance in 'y' between these two populations due to the intrinsic contribution only.

So the question is this: Is there any way that I can estimate the variance of a sample due to the intrinsic contribution from the objects, given that I know the measurement error on each data point (which differ for all the objects and in mean magnitude for the two different samples)?

2. Relevant equations

3. The attempt at a solution

Since variance is additive, if the measurement errors were the same for each object I could just use

var(intrinsic) = var(y) - var(meas)

In the presence of unequal measurement errors for each object, I was thinking that some sort of weighted form of the above equation could be used, but not sure. Been looking around for quite a few hours for a solution, but can't quite put it together in my head.

Any help, or being pointed in the right direction would be very much appreciated!

2. Jul 27, 2014