Interpret the key results for Power and Sample Size for 1 Variance

Complete the following steps to interpret Power and Sample Size for 1 Variance. Key output includes the ratio, the sample size, the power, and the power curve.

Step 1: Examine the calculated values

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.

Ratio

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.

Sample size

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.

Power

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 population comparison standard deviation or variance and the hypothesized standard deviation or variance 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.

Note

When you perform 1 Variance in Basic Statistics, Minitab displays output for both the chi-square method and the Bonett method. However, when you perform Power and Sample Size for 1 Variance, Minitab uses only the chi-square method.

Results Sample Ratio Size Power 0.8 50 0.539065 0.8 100 0.865153
Key Results: Difference, Sample Size, Power

These results show that if the ratio is 0.8 and the sample sizes are 50 and 100, then the power of the test is approximately 0.54 and 0.87, for each sample size respectively. Because 0.87 is close to 0.9, using a sample size of 100 provides adequate power for a ratio of 0.8.

Step 2: Examine the power curve

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.

Note

When you perform 1 Variance in Basic Statistics, Minitab displays output for both the chi-square method and the Bonett method. However, when you perform Power and Sample Size for 1 Variance, Minitab uses only the chi-square method.

In this graph, the power curve for a sample size of 50 shows that the test has a power of approximately 0.54 for a ratio of 0.8. For a sample size of 100, the power curve shows that the test has a power of approximately 0.87 for a ratio of 0.8. If a power of 0.87 is adequate for your situation, you should collect a sample size of 100. If you need to detect a ratio smaller than 0.8, you will need to collect a larger sample.

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