Comparing the variance of two samples with differing measurement error

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SUMMARY

The discussion centers on estimating the intrinsic variance of a sample 'y' in the presence of differing measurement errors for astronomical data. The user seeks to isolate the intrinsic contribution to variance from measurement error, which is known with high precision. The proposed method involves a weighted approach to account for unequal measurement errors, diverging from the standard additive variance formula. The user is looking for guidance on how to effectively implement this weighted variance estimation.

PREREQUISITES
  • Understanding of variance and its components in statistics
  • Familiarity with measurement error concepts in data analysis
  • Basic knowledge of statistical methods for comparing populations
  • Experience with weighted averages and their applications
NEXT STEPS
  • Research "Weighted Variance Estimation" techniques
  • Explore "Statistical Methods for Comparing Variances" in populations
  • Study "Measurement Error Models" in statistical analysis
  • Learn about "Intrinsic vs. Extrinsic Variance" in data sets
USEFUL FOR

Statisticians, astronomers, and data analysts who are working with measurement errors and variance analysis in observational data.

Astr0fiend
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Homework Statement



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)?

Homework Equations





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!
 
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