Select the analysis options for Power and Sample Size for 1-Sample Poisson Rate

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 rate of occurrence is less than the hypothesized rate. The one-sided test has greater power, but it cannot detect when the population rate is greater.

  For example, an analyst uses this one-sided test to determine whether the rate of televisions that customers return per month is less than 3. This one-sided test has greater power to determine whether the rate is less than 3, but it cannot detect whether the rate is greater than 3.

• Not equal: Use this two-sided test to determine whether the population rate differs from the hypothesized rate. 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 analyst tests whether the rate of maintenance problems for a type of aircraft is different from the target of 0.2 per day. 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 rate of occurrence is greater than the hypothesized rate. This one-sided test gives greater power, but it cannot detect whether the population rate of occurrence is less than the hypothesized rate.

  For example, a call center manager uses this one-sided test to determine whether the rate of calls per day is greater than 1000. This one-sided test has greater power to determine whether the rate is greater than 1000, but it cannot determine whether the rate is less than 1000.

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.

"Length" of observation (time, items, area, volume, etc.)

Enter a value to divide the sample rate of occurrence into a more useful form (sample rate of occurrence ÷ length of observation). For example, a manufacturer records defects quarterly, but needs to convert them into a monthly defect rate for its reports. An analyst enters 3 to divide the quarterly rate by 3 to find the monthly defect rate.