Complete the following steps to interpret a goodness-of-fit test for Poisson. Key output includes the p-value and several graphs.

To determine whether the data do not follow a Poisson distribution, compare the p-value to your significance level (α). Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that the data do not follow a Poisson distribution when the data do follow a Poisson distribution.

- P-value ≤ α: The data do not follow a Poisson distribution (Reject H
_{0}) - If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis and conclude that your data do not follow a Poisson distribution.
- P-value > α: You cannot conclude that the data do not follow a Poisson distribution (Fail to reject H
_{0}) - If the p-value is larger than the significance level, the decision is to fail to reject the null hypothesis because you do not have enough evidence to conclude that your data do not follow a Poisson distribution.

Frequencies in Observed |
---|

N | Mean |
---|---|

300 | 0.536667 |

Defects | Poisson Probability | Observed Count | Expected Count | Contribution to Chi-Square |
---|---|---|---|---|

0 | 0.584694 | 213 | 175.408 | 8.056 |

1 | 0.313786 | 41 | 94.136 | 29.993 |

2 | 0.084199 | 18 | 25.260 | 2.086 |

>=3 | 0.017321 | 28 | 5.196 | 100.072 |

Null hypothesis | H₀: Data follow a Poisson distribution |
---|---|

Alternative hypothesis | H₁: Data do not follow a Poisson distribution |

DF | Chi-Square | P-Value |
---|---|---|

2 | 140.208 | 0.000 |

In these results, the null hypothesis states that the data follow a Poisson distribution. Because the p-value is 0.000, which is less than 0.05, the decision is to reject the null hypothesis. You can conclude that the data do not come from a Poisson distribution.

Use a bar chart of observed and expected values to determine whether, for each category, the number of observed values differs from the number of expected values. Larger differences between observed and expected values indicate that the data do not follow a Poisson distribution.