Using the values of the two power function variables that you entered, Minitab calculates the ratio, the sample size, or the power of the test.
Minitab calculates the smallest ratio that you will be able to detect based on your specified power and sample size. Larger sample sizes allow you to detect smaller ratios. You want to be able to detect the smallest ratio 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 specified ratio. 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 ratio 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 two population variances or standard deviations 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 ratio is closer to 1, the test has less power to detect a difference.
Sample Size | Power | Ratio |
---|---|---|
50 | 0.9 | 2.83320 |
50 | 0.9 | 0.35296 |
These results show that if the sample size is 50 and the power value is 0.9, the test can detect ratios of approximately 2.83 and 0.35. If your situation requires the test to be able to detect a ratio closer to 1, you should increase the sample size, if possible.
Use the power curve to assess the appropriate sample size or power for your test.
The power curve represents every combination of power and ratio 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 ratio and displays the calculated value on the graph.
Examine the values on the curve to determine the ratio 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 ratio 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 ratio that you want to detect, the power also decreases.
In this graph, the power curve shows that for a sample size of 50 and a power of 0.9, the test can detect a ratio of approximately 2.8 or 0.35. As the ratio approaches 1, the power of the test decreases and approaches α (also called the significance level), which is 0.05 for this analysis.