5.8 Errors with Standard Errors

Talking about variance and sampling variance is hard, because the terms sound very similar, but have important distinctions in what they mean. For example, the “variance” is not the same as the “unbiased sample variance” which is also not the same as the “sampling variance of the sample average”. :sob:

Standard errors are a statement about the sampling variance of the sample average. But, related to this concept are the ideas of the Population Variance, the Plug-In Estimator for the Sample Variance, the Unbiased Sample Variance, and, finally, the Sampling Variance of the Sample Average (i.e the Standard Error).

How are each of these concepts related to one another, and how can we keep them all straight? As a group, fill out the following columns?

For the Estimator Properties column, here we’re considering, principally biased/unbiased and consistent/inconsistent.

Population Concept	Pop Notation	Sample Estimator	Sample Notation	Estimator Properties	Sampling Variance of Sample Estimator
Expected Value
Population Variance
Population Covariance
CEF
BLP