Example of Goodness-of-Fit Test for Poisson

A quality engineer at a consumer electronics company wants to know whether the defects per television set are from a Poisson distribution. The engineer randomly selects 300 televisions and records the number of defects per television.

  1. Open the sample data, TelevisionDefects.MTW.
  2. Choose Stat > Basic Statistics > Goodness-of-Fit Test for Poisson.
  3. In Variable, enter Defects.
  4. In Frequency variable: (optional), enter Observed.
  5. Click OK.

Interpret the results

The null hypothesis states that the data follow a Poisson distribution. Because the p-value is 0.000, which is less than the significance level of 0.05, the engineer rejects the null hypothesis and concludes that the data do not follow a Poisson distribution. The graphs indicate that the difference between the observed and expected values is large for categories 1 and 3, and that category 3 is the highest contributor to the chi-square statistic.

Poisson Goodness-of-Fit Test: Defects

Method Frequencies in Observed
Descriptive Statistics N Mean 300 0.536667 Observed and Expected Counts for Defects Poisson Observed Expected Contribution Defects Probability Count Count 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
Chi-Square Test 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

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