Example of 2-Sample Poisson Rate

An analyst for the postal service wants to compare the number of customer visits at two post offices. The analyst counts the number of customers that enter each office for 40 business days.

The analyst performs a 2-sample Poisson rate test to determine whether the daily rate of customer visits differs between the two post offices.

  1. Open the sample data, PostOfficeVisits.MTW.
  2. Choose Stat > Basic Statistics > 2-Sample Poisson Rate.
  3. From the drop-down list, select Each sample is in its own column.
  4. In Sample 1 enter Branch A.
  5. In Sample 2, enter Branch B.
  6. Click OK.

Interpret the results

The null hypothesis states that the difference in the daily rate of customer visits between the two post offices is 0. Because the p-value of 0.031 is less than the significance level (denoted as α or alpha) of 0.05, the analyst rejects the null hypothesis and concludes that the daily rate of customer visits differs between the two post offices. The 95% CI indicates that Branch B is likely to have a higher rate of customer visits than Branch A.

Test and CI for Two-Sample Poisson Rates: Branch A, Branch B

Method λ₁: Poisson rate of Branch A λ₂: Poisson rate of Branch B Difference: λ₁ - λ₂
Descriptive Statistics Total Sample N Occurrences Sample Rate Branch A 40 9983 249.575 Branch B 40 10291 257.275
Estimation for Difference Estimated 95% CI for Difference Difference -7.7 (-14.6768, -0.723175)
Test Null hypothesis H₀: λ₁ - λ₂ = 0 Alternative hypothesis H₁: λ₁ - λ₂ ≠ 0
Method Z-Value P-Value Exact 0.031 Normal approximation -2.16 0.031
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