Re: Difference b/w Standard Deviation and Variance


Reef Fish wrote:
DarkProtoman wrote:
What is the difference b/w the standard deviation and the variance
(other than the way they're calculated)? Like when are they used, or
when is one preferred over the other? Thanks!!!!

Good practical question!

Standard deviation is measured in the units in which the data is
measured.
That's why a confidence interval is in +- number of standard dev.
units.

It's more than just a preference. You can't calculate the standard
deviation
without calculating the variance first, by taking the square root of
it.

When is a variance prefered? Can't think of a good answer right off
hand.
It's used more for theoretical reasons than for practical usage. For
example,
the sample variance is an unbiased estimate of the variance, but nobody
I know ever uses an unbiased estimate of a standard deviation in
practice.

It's used in regression and other methods in breaking down the total
variation into component parts. I am sure others will name other
"prefered" uses of it.

Related to this last idea is that the variance may be used to assess
the equal variance assumption of the two sample t-test. This is
through the variance ratio. When the ratio is large Welch's modified
t-test is often recommended.

In terms of intuitive interpretation, standard deviation wins.

--
Kevin E. Thorpe
Assistant Professor, Department of Public Health Sciences
Faculty of Medicine, University of Toronto

.

Relevant Pages

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