# Effective sample size of a weighted sample

I am trying to understand the meaning of the effective sample size when we have weights for the sample. I have an intuitive understanding of why effective sample size can be less than the raw sample size when correlations exist in the data, but can somebody please explain why this is the case when the sample is weighted? Can weights be regarded as introducing some kind of correlation into the data? Thanks!

• An illustration: if I have five samples, and weight one of them at zero, I effectively have four samples. – James Phillips Oct 16 '18 at 15:14
• That's an extreme example. Also, when we weight a sample, we usually make sure that the sum of the targets for different exclusive cuts add up to 1. In your example, if we weight one respondent to 0, the other 4 should be weighted up by a factor of 1.25. – Payam Bagheri Oct 17 '18 at 18:02
• Our weights might be for different purpose, as I use regression weights to represent the statistical uncertainty in a sample's value where the greater the uncertainty the smaller the weight. My example was meant to illustrate effective sample size and not as a discussion of statistical uncertainty in relation to weighted regression. – James Phillips Oct 17 '18 at 18:13