Target: Check if the statistical model fits the observations.

The test uses Chi-square distribution.

Example: checking a fair dice.

Model: the probability of each side is equal - 1/6.

H0: fair dice.

H1: unfair dice.

The **groups** are the dice's numbers (1,2,3,4,5,6).

In this example, you throw the dice n times.**Expected frequencies** - for each group is n/6.**Observed frequencies** - the actual times each number appears.

H_{0}: Model Fits | |

H_{1}: Model Doesn't Fit | |

Degree Of Freedom (DF) = n - m - 1

tails: For the Goodness of Fit Test, you can use only the right tail test.

Expected Value - choose **Expected Frequencies** or **Expected Probabilities**.

Group | Observed Frequency | Expected Value |
---|---|---|

The sum of the **expected frequencies/probabilities** must be equal to the sum of the **observed frequencies** or to **one**.

You may copy data from Excel, Google sheets or any tool that separate data with **Tab** and **Line Feed**.

Copy the data, **one block** of **3** consecutive columns includes the top **header row** and left **header column**, and paste below.

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k: | number of groups | |

n: | sample size | |

χ² | Chi square test statistic |

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