Hello,(adsbygoogle = window.adsbygoogle || []).push({});

it is well-known that the Chi-square test between an observed distributionOand an expected distributionEcan be interpreted as a test based on (twice) the second order Taylor approximation of the Kullback-Leibler divergence, i.e.: [tex]2\,\mathcal{D}_{KL}(O \| E) \approx \sum_i \frac{(O_i-E_i)^2}{E_i} = \chi^2[/tex]

whereiis the bin of the histogram (or contigency table). A proof is given here (page 5).

The question is: how do we know that each of the error terms [itex]\frac{(O_i-E_i)^2}{E_i}[/itex] on the right side of the above equation follows a normal distributionN(0,1)? There is probably some some assumption to be made...?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Chi-square test: why does it follow a Chi-square distribution

Loading...

Similar Threads - square test does | Date |
---|---|

I Online sourses to learn chi square test of homogeneity | Feb 9, 2017 |

A Outliers categorical data? | Dec 3, 2016 |

I About chi-squared and r-squared test for fitting data | Nov 2, 2016 |

A Chi squared test for data with error | Jun 16, 2016 |

Can a Chi2 test be used on uniform p test results? | Aug 14, 2015 |

**Physics Forums - The Fusion of Science and Community**