Select the analysis options for Power and Sample Size for 1 Variance

Select the alternative hypothesis or specify the significance level 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 the population standard deviation or population variance is less than the hypothesized standard deviation or hypothesized variance. This one-sided test has greater power than a two-sided test, but it cannot detect whether the population standard deviation or population variance is greater than the hypothesized value.

  For example, a logistics analyst uses this one-sided test to determine whether the standard deviation of shipping weights is less than 8.8 kg. This one-sided test has greater power to determine whether the standard deviation is less than 8.8, but it cannot detect whether the standard deviation is greater than 8.8.

• Not equal: Use this two-sided test to determine whether the population standard deviation or the population variance differs from the hypothesized standard deviation or variance. This two-sided test can detect differences that are less than or greater than the hypothesized value, but it has less power than a one-sided test.

  For example, a quality analyst tests whether the variance of fill volumes is different from the target of 2.5. Because any difference from the target is important, the analyst tests whether the difference is greater than or less than the target.

• Greater Than: Use this one-sided test to determine whether the population standard deviation or population variance is greater than the hypothesized standard deviation or hypothesized variance. This one-sided test has greater power, but it cannot detect when the population standard deviation or population variance is less than the hypothesized standard deviation or hypothesized variance.

  For example, an analyst uses this one-sided test to determine whether the standard deviation of pipe diameters is greater than 2 mm. This one-sided test has greater power to determine whether the variance is greater than 2 mm, but it cannot determine whether the variance is less than 2 mm.

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.