Select the analysis options for Power and Sample Size for 2-Sample t

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 one population mean is less than another population mean. This one-sided test has greater power than a two-sided test, but it cannot detect whether one population mean is greater than another population mean. If you select this option, enter negative values in Differences on the Power and Sample Size for 2-Sample t dialog box.

  For example, an engineer uses this one-sided test to determine whether the mean difference in strength of plastic sheeting from two suppliers is less than 0. This one-sided test has greater power to detect whether the difference in strength is less than 0, but it cannot detect whether the difference is greater than 0.

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

  For example, a bank manager wants to know whether the mean customer satisfaction ratings at two banks differ. Because any difference in the ratings is important, the manager uses this two-sided test to determine whether the rating at one bank is greater than or less than the rating of the other bank.

• Greater than: Use this one-sided test to determine whether one population mean is greater than another population mean. This one-sided test has greater power than a two-sided test, but it cannot detect whether one population mean is less than another population mean. If you select this option, enter positive values in Differences on the Power and Sample Size for 2-Sample t dialog box.

  For example, a technician uses a one-sided test to determine whether the mean difference between the speeds of two filling machines is greater than 0 seconds per box. This one-sided test has greater power to detect whether the difference in speed 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.