Using the values of the two power function variables that you entered, Minitab calculates the comparison rate, the sample size, or the power of the test.
Minitab calculates the comparison rate. The difference between the comparison rate and the baseline rate is the minimum difference for which you can achieve the specified level of power for each sample size. Larger sample sizes enable the test to detect smaller differences. You want to detect the smallest difference that has practical consequences for your application.
Minitab calculates how large your sample must be for a test with your specified power to detect the difference between the baseline rate and comparison rate. Because sample sizes are whole numbers, the actual power of the test might be slightly greater than the power value that you specify.
If you increase the sample size, the power of the test also increases. You want enough observations in your sample to achieve adequate power. But you don't want a sample size so large that you waste time and money on unnecessary sampling or detect unimportant differences to be statistically significant.
Minitab calculates the power of the test based on the specified comparison rate and sample size. A power value of 0.9 is usually considered adequate. A value of 0.9 indicates you have a 90% chance of detecting a difference between the population rates when a difference actually exists. If a test has low power, you might fail to detect a difference and mistakenly conclude that none exists. Usually, when the sample size is smaller or the difference is smaller, the test has less power to detect a difference.
Comparison Rate | Sample Size | Target Power | Actual Power |
---|---|---|---|
32 | 79 | 0.9 | 0.902793 |
38 | 86 | 0.9 | 0.902550 |
These results show that if the power of the test is 0.9 and the comparison rates are 32 and 38, you should collect sample sizes of 79 and 86, for each comparison rate respectively. Therefore, to ensure the test has adequate power to detect both comparison rates, you should collect a sample size of 86. Because the target power value of 0.9 results in a sample size that is not an integer, Minitab also displays the power (Actual Power) for the rounded sample size.
Use the power curve to assess the appropriate sample size or power for your test.
The power curve represents every combination of power and comparison rate for each sample size when the significance level is held constant. Each symbol on the power curve represents a calculated value based on the values that you enter. For example, if you enter a sample size and a power value, Minitab calculates the corresponding comparison proportion and displays the calculated value on the graph.
Examine the values on the curve to determine the difference between the comparison rate and the baseline rate that can be detected at a certain power value and sample size. A power value of 0.9 is usually considered adequate. However, some practitioners consider a power value of 0.8 to be adequate. If a hypothesis test has low power, you might fail to detect a difference that is practically significant. If you increase the sample size, the power of the test also increases. You want enough observations in your sample to achieve adequate power. But you don't want a sample size so large that you waste time and money on unnecessary sampling or detect unimportant differences to be statistically significant. If you decrease the size of the difference that you want to detect, the power also decreases.
In this graph, the power curve shows that to detect a comparison rate of 32 with a power of 0.9, the sample size needs to be 79. To detect a comparison rate of 38 with a power of 0.9, the sample size needs to be 86. As the comparison rate approaches the baseline rate (35, in this graph), the power of the test decreases and approaches α (also called the significance level), which is 0.05 for this analysis.