Select the analysis options for Power and Sample Size for Paired 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 the difference in paired means is less than the hypothesized difference. This one-sided test has greater power than a two-sided test, but it cannot detect whether the difference is greater than the hypothesized difference.

  For example, a baker tests uses this one-sided test to determine whether bread that is baked at a lower temperature for more time contains less moisture. The baker divides samples from a single batch of dough in half and bakes each half at different temperatures for different times. This one-sided test has greater power to determine whether the bread baked at a lower temperature has less moisture, but it cannot detect whether the bread contains more moisture.

• Not equal: Use this two-sided test to determine whether the difference in paired means is different from the hypothesized difference. 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, an engineer compares the difference in measurements of the same bearings made with 2 different calipers. Because any difference in the measurements is important, the engineer uses this two-sided test to determine whether the difference is greater than or less than 0.

• Greater than: Use this one-sided test to determine whether the difference between paired means is greater than the hypothesized difference. This one-sided test has greater power than a two-sided test, but it cannot detect whether the difference is less than the hypothesized difference.

  For example, a quality analysis uses this one-sided test to determine whether treated wood beams are stronger than untreated beams. Each beam is cut in half; one half is treated and the other half is untreated. This one-sided test has greater power to determine whether the treated wood beams are stronger than the untreated beams, but it cannot detect whether the treated beams are less strong than the untreated beams.

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.