Select the analysis options for Power and Sample Size for 2-Sample Poisson Rate

Stat > Power and Sample Size > 2-Sample Poisson Rate > Options

Select the alternative hypothesis, specify the significance level for the test, or specify the length of observation.

Alternative Hypothesis

From Alternative Hypothesis, select the hypothesis that you want to test:
  • Less than (R1 < R2): Use this one-sided test to determine whether one population rate is less than another population rate. This one-sided test has greater power than a two-sided test, but it cannot detect whether one population rate is greater than another population rate. If you select this option, the value you enter for Comparison rates (R1) must be less than the value you enter for Baseline rate (R2) on the Power and Sample Size for 2-Sample Poisson Rate dialog box.

    For example, an analyst uses this one-sided test to determine whether the difference in repairs per year for two copiers is less than 0. This one-sided test has greater power to detect whether the difference in repairs is less than 0, but it cannot detect whether the difference is greater than 0.

  • Not equal (R1 ≠ R2): Use this two-sided test to determine whether two population rates are not equal. This two-sided test can detect whether one population rate is less than or greater than another population rate, but it has less power than a one-sided test.

    For example, a quality analyst tests whether the calls per day to two call centers differ. Because any difference in the calls is important, the analyst uses this two-sided test to determine whether the rate at one call center is greater than or less than the rate at the other call center.

  • Greater than (R1 > R2): Use this one-sided test to determine whether one population rate is greater than another population rate. This one-sided test has greater power than a two-sided test, but it cannot detect whether one population rate is less than another population rate. If you select this option, the value you enter for Comparison rates (R1) must be greater than the value you enter for Baseline rate (R2) on the Power and Sample Size for 2-Sample Poisson Rate dialog box.

    For example, a technician uses this 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.

"Lengths" 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).
  • When the samples use the same units, enter 1 value to convert both samples.
  • When the samples use different units, enter 2 values to convert the units into the same unit.
For example, the first sample represents defects per quarter and the second sample represents defects per month. To convert both samples to defects per month, enter 3 1. Minitab divides the quarterly rate by 3 to convert it to a monthly rate. Minitab divides the monthly rate by 1, which does not change the rate.
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