Interpret the key results for 2-Sample Poisson Rate

Complete the following steps to interpret a 2-sample Poisson rate test. Key output includes the estimate for difference, the confidence interval, and the p-value.

In This Topic

Step 1: Determine a confidence interval for the difference in population rates
Step 2: Determine whether the difference is statistically significant

Step 1: Determine a confidence interval for the difference in population rates

First, consider the difference in the sample rates, and then examine the confidence interval.

The estimated difference is an estimate of the difference in the population rates of occurrence. Because the difference is based on sample data and not on the entire population, it is unlikely that the sample difference equals the population difference. To better estimate the population difference, use the confidence interval for the difference.

The confidence interval provides a range of likely values for the difference between two population rates of occurrence. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population difference. The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size. For more information, go to Ways to get a more precise confidence interval.

Estimation for Difference

Estimated Difference	95% CI for Difference
-7.7	(-14.6768, -0.723175)

Key Results: Estimated difference, 95% CI for difference

In these results, the estimate of the population rate of occurrence for the difference in customer visits for two post offices is −7.7. You can be 95% confident that the difference in population rates is between approximately −14.7 and −0.7.

Step 2: Determine whether the difference is statistically significant

To determine whether the difference between the rates of occurrence is statistically significant, compare the p-value to the significance level. 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 a difference exists when there is no actual difference.

P-value ≤ α: The difference between the rates is statistically significant (Reject H₀): If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis. You can conclude that the difference between the population rates does not equal the hypothesized difference. If you did not specify a hypothesized difference, Minitab tests whether there is no difference between the rates (Hypothesized difference = 0). Use your specialized knowledge to determine whether the difference is practically significant. For more information, go to Statistical and practical significance.
P-value > α: The difference between the rates is not statistically significant (Fail to reject H₀): If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the population rates are different. You should make sure that your test has enough power to detect a difference that is practically significant. For more information, go to Power and Sample Size for 2-Sample Poisson Rate.

Test

Null hypothesis	H₀: λ₁ - λ₂ = 0
Alternative hypothesis	H₁: λ₁ - λ₂ ≠ 0

Method	Z-Value	P-Value
Exact		0.031
Normal approximation	-2.16	0.031

Key Result: P-Value

In these results, the null hypothesis states that the difference in the number of customers between the two post offices is 0. Because the p-value of 0.031 is less than the significance level of 0.05, the analyst rejects the null hypothesis and concludes that the number of customers differs between the two post offices. The 95% CI indicates that Branch B is likely to have a higher rate of customers than Branch A.