Select the analysis options for 2-Sample Poisson Rate

Stat > Basic Statistics > 2-Sample Poisson Rate > Options

Specify the confidence level for the confidence interval, the hypothesized difference, the alternative hypothesis, and the test method, and enter the lengths of observation.

Confidence level

In Confidence level, enter the level of confidence for the confidence interval.

Usually, a confidence level of 95% works well. A 95% confidence level indicates that, if you take 100 random samples from the population, the confidence intervals for approximately 95 of the samples will contain the population difference.

For a given set of data, a lower confidence level produces a narrower confidence interval, and a higher confidence level produces a wider confidence interval. The width of the interval also tends to decrease with larger sample sizes. Therefore, you may want to use a confidence level other than 95%, depending on your sample size.
  • If your sample size is small, a 95% confidence interval may be too wide to be useful. Using a lower confidence level, such as 90%, produces a narrower interval. However, the likelihood that the interval contains the population difference decreases.
  • If your sample size is large, consider using a higher confidence level, such as 99%. With a large sample, a 99% confidence level may still produce a reasonably narrow interval, while also increasing the likelihood that the interval contains the population difference.

Hypothesized difference

Enter a value in Hypothesized difference. The hypothesized difference defines your null hypothesis. Think of this value as a target value or a reference value. For example, a company wants to know whether the number of calls per day at one call center is at least 100 more than the number at another center (H0: λcenter1: λ center2 = 100).

Alternative hypothesis

From Alternative hypothesis, select the hypothesis that you want to test:
Difference < hypothesized difference

Use this one-sided test to determine whether the difference in the population rates of occurrence of sample 1 and sample 2 is less the hypothesized difference, and to get an upper bound. 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, an analyst uses this one-sided test to determine whether the difference in repairs per year for two copiers is less than 2. This one-sided test has greater power to detect whether the difference in repairs is less than 2, but it cannot detect whether the difference is greater than 2.

Difference ≠ hypothesized difference

Use this two-sided test to determine whether the difference in population rates differs from the hypothesized difference, and to get a two-sided confidence interval. This two-sided test can detect differences that are less than or greater than the hypothesized difference, 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.

Difference > hypothesized difference

Use this one-sided test to determine whether the difference between population rates of sample 1 and sample 2 is greater than the hypothesized difference, and to get a lower bound. 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 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.

Test method

From Test method, select the method for estimating the rates. When the samples are equal and large, the default method, Estimate the rates separately, is preferred. If the samples are equal but small, the default method is less accurate.

Select Use the pooled estimate of the rate only when the Hypothesized difference is equal to 0. When you select the pooled method, Minitab calculates the confidence interval based on the default method of estimating the rates separately, not on the pooled estimate of the rate.

Lengths of observation

Enter a value to specify the observation period (time, area, volume, number of items) for the count data. By default, Minitab uses a value of 1, but you can enter a different value to express the sample rate of occurrence into a more useful form.
  • When the samples use the same units, enter one value to convert both samples. If you enter a length of observation other than 1, convert the Hypothesized difference. For example, if your unconverted hypothesized difference is 15 defects per quarter and your length of observation is 3 for both samples, enter the converted rate of 5 (15 ÷ 3) defects per month for the Hypothesized difference.
  • When the samples use different units, enter two 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 into a monthly rate. Minitab divides the monthly rate by 1, which does not change the rate.

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