Example of Goodness-of-Fit Test for Poisson
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An insurance agent wants to use a U chart to monitor the number of accidents per month at a particular intersection. Because a U chart assumes that data follow a Poisson distribution, the agent wants to assess whether the number of accidents follow a Poisson distribution. The agent records the number of accidents per month at this intersection for 50 months.

1    Open the worksheet ACCIDENT.MTW.

2    Choose Stat > Basic Statistics > Goodness-of-Fit Test for Poisson.

3    In Variable, enter Accidents.

4    Click OK.

Session window output

Goodness-of-Fit Test for Poisson Distribution

 

 

Data column: Accidents

 

Poisson mean for Accidents = 2.24

 

                         Poisson            Contribution

Accidents  Observed  Probability  Expected     to Chi-Sq

0                 7     0.106459    5.3229       0.52839

1                 8     0.238467   11.9234       1.29097

2                13     0.267083   13.3542       0.00939

3                10     0.199422    9.9711       0.00008

>=4              12     0.188569    9.4285       0.70136

 

 

 N  N*  DF   Chi-Sq  P-Value

50   0   3  2.53020    0.470

Graph window output

 

Interpreting the results

Minitab calculates each category's contribution to the chi-square value as the square of the difference in the observed and expected values for a category divided by the expected value for that category. The largest difference between the observed and expected value is for the category with 1 accident and is the highest contributor to the chi-square statistic. However, the contribution is not enough to reject the null hypothesis. If you choose an a-level of 0.05, the p-value for this test is 0.470, which is greater than 0.05. Therefore, you can conclude that you do not have enough evidence to reject that the number of accidents at a particular intersection follow a Poisson distribution.

Note

The chi-square test is an approximate test and the test result may not be valid when the expected value for a category is less than 5. If one or more categories have expected values less than 5, you can combine them with adjacent categories to achieve the minimum required expected value.