#### Central Limit Theorem (created 2004-03-09).

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*Dear Professor Mean, How does the central limit theorem affect the
statistical tests that I might use for my data?*

The Central Limit Theorem tells you about how an average from a random
sample behaves. For most situations, the average from a random sample will
tend towards a normal distribution (bell-shaped curve) as the sample size
increases, even if the individual data values follow a different
distribution.

How quickly the average converges to a normal distribution depends on what
the individual data look like. Highly skewed data and/or data with
outliers will tend to converge more slowly. If your data has no outliers and
is reasonably symmetric, then convergence will be very fast.

If your sample size is large, then you should be more comfortable with
using parametric statistics, like a t-test or analysis of variance, because
you can be reasonably confident that the averages used in the t-test or
analysis of variance, are reasonably close to a normal distribution.

**Further reading**

The first four references give nice computer simulations of the central
limit theorem. The last two references gives the detailed mathematical
conditions for the central limit theorem.

**
Central Limit Theorem. Example: Uniform.**. Annis C. Accessed on
2004-03-09. www.statisticalengineering.com/central_limit_theorem.htm
**The
Central Limit Theorem in Action**. Krider D. Accessed on
2004-03-09. www.rand.org/methodology/stat/applets/clt.html
**Central
Limit Theorem**. Lowry R, Vassar College. Accessed on 2004-03-09.
faculty.vassar.edu/lowry/central.html
**Central
Limit Theorem Applet**. Ogden RT, Department. of Statistics,
University of South Carolina. Accessed on 2004-03-09. www.stat.sc.edu/~west/javahtml/CLT.html
**
Central Limit Theorem**. Weisstein EW. Accessed on 2004-03-09.
www.itu.dk/bibliotek/encyclopedia/math/c/c181.htm
**
Central limit theorem**. Wikipedia. Accessed on 2004-03-09.
en.wikipedia.org/wiki/Central_limit_theorem