EngineRoom

1 Sample Poisson Rate Test

When to use this tool

Use the Poisson Rate test to determine whether the rate of occurrence of events in a given interval of space or time is significantly different from a specified rate. You can use this test with raw data (the number of occurrences each period), with a frequency variable, or with summary statistics (sample size and number of occurrences.)

The assumptions of the one-sample Poisson rate test are:

  1. The data are counts (discrete) that follow the Poisson distribution.
  2. The sample is a simple random sample from its population. Each individual in the population has an equal probability of being selected in the sample.
  3. The mean occurrence rate is constant.

As an example, a web retail company call center has recently initiated an artificial intelligence (AI) system to handle customer calls that passes along any unresolved calls to human associates. Data collected over the last 30 days since the program was released shows the average number (rate) of unresolved calls was 4.13/day. The company wants to test whether the rate of unresolved calls getting through to the humans exceeds its expected average rate of 5/day.

Using EngineRoom

Click to Download Data File

The data set consists of the number of customer calls per day passed along to the human associate by the AI system.

Column of numbers showing the number of customer calls

Select the Poisson Rate test from the Parametric menu under Analyze.

Example:

Note: This example has the Guided Mode disabled, so it combines some steps in one dialog box. You can enable or disable Guided Mode from the User menu on the top right of the EngineRoom workspace.

Steps:

  • Select the Analyze menu > Parametric > 1 Sample Poisson Rate Test
  • Drag the Customer Calls variable onto the Event Counts drop zone on the study:
Dragging Customer Calls variable on the Event counts dropzone
  • Change any test setup options - in this example, leave them at their defaults, but change Hypothesized Rate of Occurrence to 5.
Set up screen for 1 Sample Poisson Rate test showing the not equal alternative hypothesis and a hypothesized rate of 5
  • Click Continue to see the 1 Sample Poisson Rate test output:
Output of Poisson Rate Test showing the p-value is within the reject region and the hypothesized rate is outside the confidence interval

Within the output you can see:

  • The Conclusion Statement: This will evaluate the p-value and conclude whether to reject or fail to reject the null hypothesis.
  • Tables of Numeric Data: This includes the test statistic and the confidence interval, allowing you to cross-reference the conclusion and provides additional details.
  • Visual Representations of the Conclusion: These graphs provide another way to understand the conclusion by comparing the p-value to the test region, as well as the Hypothesized Rate to the calculated confidence interval.

1 Sample Poisson Rate Video Tutorial

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