Step 1: Determine a confidence interval for the difference in population proportions
First, consider the difference in the sample proportions, and then examine the confidence interval.
The difference is an estimate of the difference in the population proportions. 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 proportions. 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 population proportions 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 proportions 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 proportions does not equal the hypothesized difference. If you did not specify a hypothesized difference, Minitab tests whether there is no difference between the proportions (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 proportions is 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 difference between the population proportions is statistically significant. 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 Proportions.
Minitab uses the normal approximation method and Fisher's exact method to calculate the p-values for the 2 proportions test. If the number of events and the number of nonevents is at least 5 in both samples, use the smaller of the two p-values. If either the number of events or the number of nonevents is less than 5 in either sample, the normal approximation method may be inaccurate. Fisher's exact method is valid for all samples, but tends to be conservative. A conservative p-value understates the evidence against the null hypothesis.