Select the analysis options for Power and Sample Size for 2 Variances

Stat > Power and Sample Size > 2 Variances > Options

Select the alternative hypothesis, specify the significance level, or select the method for the test.

Alternative Hypothesis

From Alternative Hypothesis, select the hypothesis that you want to test:
  • Less Than: Use this one-sided test to determine whether one population standard deviation or population variance is less than another population standard deviation or population variance. This one-sided test gives greater power, it cannot detect whether one population standard deviation or population variance is greater than another population standard deviation or population variance. If you select this option, enter values less than 1 in Ratios on the Power and Sample Size for 2 Variances dialog box.

    For example, an analyst uses this one-sided test to determine whether the standard deviation of a new machine's performance is less than the standard deviation of an old machine's performance. This one-sided test has greater power to detect whether the ratio in standard deviations is less than 1, but it cannot detect whether the ratio is greater than 1.

  • Not equal: Use this two-sided test to determine whether two population standard deviations or two population variances are not equal. This two-sided test can detect whether one population standard deviation or population variance is less than or greater than another population standard deviation or population variance, but it has less power than a one-sided test.

    For example, a healthcare consultant wants to compare the variances of patient satisfaction ratings from two hospitals. Because any difference in the variances is important, the consultant uses this two-sided test to determine whether the variance at one location is greater than or less than the other location.

  • Greater Than: Use this one-sided test to determine whether one population standard deviation or population variance is greater than another population standard deviation or population variance. This one-sided test has greater power than a two-sided test, but it cannot detect whether one population standard deviation or population variance is less than another population standard deviation or population variance. If you select this option, enter values greater than 1 in Ratios on the Power and Sample Size for 2 Variances dialog box.

    For example, an analyst tests whether the variance in an old extrusion machine is greater than the variance in a new extrusion machine. This one-sided test has greater power to detect whether the ratio is greater than 1, but it cannot detect whether the ratio is less than 1.

For more information on selecting a one-sided or two-sided alternative hypothesis, go to About the null and alternative hypotheses.

Significance level

Use the significance level to minimize the power value of the test when the null hypothesis (H0) is true. Higher values for the significance level give the test more power, but also increase the chance of making a type I error, which is rejecting the null hypothesis when it is true.

Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates that the risk of concluding that a difference exists—when, actually, no difference exists—is 5%. It also indicates that the power of the test is 0.05 when there is no difference.
  • Choose a higher significance level, such as 0.10, to be more certain that you detect any difference that possibly exists. For example, a quality engineer compares the stability of new ball bearings with the stability of current bearings. The engineer must be highly certain that the new ball bearings are stable because unstable ball bearings could cause a disaster. Therefore, the engineer chooses a significance level of 0.10 to be more certain of detecting any possible difference in the stability of the ball bearings.
  • Choose a lower significance level, such as 0.01, to be more certain that you detect only a difference that actually exists. For example, a scientist at a pharmaceutical company must be very certain that a claim that the company's new drug significantly reduces symptoms is true. The scientist chooses a significance level of 0.01 to be more certain that any significant difference in symptoms does exist.

Method

Select the method that Minitab uses to analyze the data. The F-test is based on the normal distribution, and is accurate only for normally distributed data. Any departure from normality can cause this test to yield inaccurate results. However, if the data conform to the normal distribution, then the F-test is typically more powerful than Levene's test.

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