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.

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

Method

λ₁: Poisson rate of Branch A
λ₂: Poisson rate of Branch B
Difference: λ₁ - λ₂

Descriptive Statistics

Sample	N	Total Occurrences	Sample Rate
Branch A	40	9983	249.575
Branch B	40	10291	257.275

Estimation for Difference

Estimated Difference	95% CI for 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