# Chi2 test
When checking the normality of a distribution our first intuition would be to draw a histogram of the distribution of the observed variables to see how closely it resembles a normalized Gaussian curve. 

![chi21](baseUrl/statsDescriptives/chi2/chi21.png)


This is the exact principle behind the Chi2 test that adds to this intuition a small dose of statistical calculations.  The principle is as follows:

![chi22](baseUrl/statsDescriptives/chi2/chi22.png)

![equation](d_i=(N_i-"NP"_i)^2/"NP"_i)

For each bar of the histogram we can calculate:

- Ni: The number of parts actually observed (here 10)
- Npi: The number of parts theoretically observed if it were a normal distribution (here 9.2)
- ![equationInline](d_i=(N_i-"NP"_i)^2/"NP"_i)
represents the “number of badly arranged parts”

We then calculate  ![equationInline](D=sumD_i)
,and find that D follows a distribution law due to the n-2 degrees of freedom (N being the number of classes). Consequently, we can calculate the probability of getting such a value

![courbe chi2](baseUrl/statsDescriptives/chi2/courbe-chi2.jpg)


For example; for a histogram composed of 7 classes, if we calculated one d at 11.07 then we calculate that there are 5% that obtain this value, or more if the distribution law for the parts is actually normal. 

The result of the test would therefore be 5% and we generally conclude in the following way:
- If X < 5%: the variables distribution law is not considered to follow a normal distribution
- If X >= 5%: the normality hypothesis is accepted and we consider that this distribution law follows a normal distribution. 


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Chi2 test

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