# Select the analysis options for Power and Sample Size for 2 Proportions

Stat > Power and Sample Size > 2 Proportions > Options

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 (p1 < p2): Use this one-sided test to determine whether one population proportion is less than another population proportion. This one-sided test has greater power than a two-sided test, but it cannot detect whether one population proportion is greater than another population proportion. If you select this option, the value you enter for Comparison proportions (p1) must be less than the value you enter for Baseline proportion (p2) on the Power and Sample Size for 2 Proportions dialog box.

For example, an engineer uses this one-sided test to determine whether the difference between the proportions of defective parts from two grades of material is less than 0. This one-sided test has greater power to detect whether the difference in proportions of defective parts is less than 0, but it cannot detect whether the difference is greater than 0.

• Not equal (p1 ≠ p2): Use this two-sided test to determine whether two population proportions are not equal. This two-sided test can detect whether one population proportion is less than or greater than another population proportion, but it has less power than a one-sided test.

For example, a bank manager tests whether the proportion of customers who have savings accounts differs at two locations. Because any difference in the proportions is important, the manager uses this two-sided test to determine whether the proportion at one location is greater than or less than the other location.

• Greater than (p1 > p2): Use this one-sided test to determine whether one population proportion is greater than another population proportion. This one-sided test has greater power than a two-sided test, but it cannot detect whether one population proportion is less than another population proportion. If you select this option, the value you enter for Comparison proportions (p1) must be greater than the value you enter for Baseline proportion (p2) on the Power and Sample Size for 2 Proportions dialog box.

For example, a logistics analyst uses a one-sided test to determine whether the difference in the proportions of on-time packages for two locations is greater than 0. This one-sided test has greater power to detect whether the difference in on-time deliveries is greater than 0, but it cannot detect whether the difference is less than 0.

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.
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