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.
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.