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.
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.
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.
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Phil Ender, 30Jun98