Interpret the key results for Goodness-of-Fit Test for Poisson

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

Step 1: Determine whether the data do not follow a Poisson distribution

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 H0)
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 H0)
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.

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

Key Result: P-Value

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.

Step 2: Examine the difference between observed and expected values for each category

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.

This bar chart indicates that the observed values for 0 defects, 1 defect, and more than 3 defects are different from the expected values. Thus, the bar chart visually confirms what the p-value indicates, which is that the data do not follow a Poisson distribution.

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