### chi-squared test

**(χ² test, Pearson's chi-squared test)**
(statistical significance test)

The **chi-squared test** (**χ²**)
is a statistical test for significance, e.g.,
for application to data from observations,
to see if it gives significant support to
a particular hypothesis or not.

Essentially, it consists of normalizing the
data, summing the squares of the normalized
data (the **chi-squared**),
and using the resulting total to test
for a degree of significance.
Minimum chi-squared values have been calculated or
can be calculated to indicate significance,
from the number of categories in the
hypothesis and the degree of significance
one is looking for.

For example, if you hypothesize that most
star-systems are binary, pick a hundred
star-systems at random and check to
see how many are binary, and wish to know
whether these results indicate
at least 95% chance that your hypothesis
is true, you can calculate **chi-squared**
and compare it with an appropriate
value indicating 95% probability.

There are variants of the chi-squared test,
but what is generally meant without other
qualification is **Pearson's chi-squared test**.

(*statistics*)
**Further reading:**

http://en.wikipedia.org/wiki/Chi-squared_test

**Referenced by pages:**

PSF fitting

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