Introduction to Research Design and Statistics

A Tale of Three Variances


The Population Variance

This is the variance of the entire population. Often the population variance is unknown or, in fact, unknowable. It is usually denoted with the Greek symbol sigma-squared, σ2.

variance formula

The Variance of the Sample

This is the variance of a particular sample. It is not usually used because what researchers are really interested in is estimating the population variance from sample data. The formula is the same as for the population variance. It is usually denoted using the Roman letters s-squared, s2.

variance formula

The Unbiased Estimate of the Population Variance

This is the variance you want to use. The formula uses (n - 1) in the denominator to yield an unbiased estimate of the population variance. It's symbol can be the same as the sample variance, s2, or sometimes using sigma with a caret over it. We will use s2 and will not get it confused with the variance of the sample because we are not interested in the variance of the sample per se.

variance formula


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Phil Ender, 30Jun98