Hi everybody.

I've been trying to replicate some tests that I use in Minitab in R/RStudio.

This time I got the 2 sample Poisson Test.

Situation: "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."

(See below the data used in this analysis)

Performing the analysis I've got the same p-value for both analysis:

R: p-value = 0.03107

Minitab: P-Value 0.031

(Well, I hope I've performed the test in R in the correct way).

**My point is the Confidence Interval (CI).**

I undestand what the CI means and the interpretation for that but I don't know why the CI results are different.

Any commnents will be helpful.

Thank you.

**See below the complete analysis' results for the Poisson test.**

R's Results

poisson.test(c(sum(BranchA), sum(BranchB)), c(40, 40),

alternative = "two.sided", conf.level = 0.95)

**Comparison of Poisson rates**

data: c(sum(BranchA), sum(BranchB)) time base: c(40, 40)

count1 = 9983, expected count1 = 10137, p-value = 0.03107

alternative hypothesis: true rate ratio is not equal to 1

95 percent confidence interval:

0.9436314 0.9972484

sample estimates:

rate ratio

0.9700709

You can find this Minitab's example here

Minitab's Results

Method

lambda1: Poisson rate of BranchA

lambda2: Poisson rate of BranchB

Difference: lambda1 - lambda2

Descriptive Statistics

Total

Sample N Occurrences Sample Rate

BranchA 40 9983 249.575

BranchB 40 10291 257.275

Estimation for Difference

Estimated 95% CI for

Difference Difference

-7.7 (-14.6768, -0.723175)

Test

Null hypothesis H0: lambda1 - lambda2 = 0

Alternative hypothesis H1: lambda1 - lambda2 ≠ 0

Method Z-Value P-Value

Exact 0.031

Normal approximation -2.16 0.031

Data

BranchA | BranchB |
---|---|

268 | 247 |

266 | 257 |

252 | 273 |

259 | 269 |

271 | 207 |

279 | 258 |

237 | 260 |

226 | 262 |

278 | 243 |

249 | 264 |

246 | 236 |

217 | 253 |

223 | 235 |

250 | 236 |

244 | 265 |

259 | 247 |

247 | 271 |

268 | 274 |

275 | 276 |

241 | 264 |

265 | 265 |

249 | 244 |

274 | 267 |

245 | 247 |

210 | 267 |

231 | 274 |

207 | 270 |

251 | 267 |

257 | 287 |

249 | 277 |

233 | 223 |

273 | 257 |

236 | 282 |

257 | 269 |

232 | 250 |

243 | 248 |

248 | 283 |

255 | 224 |

255 | 257 |

258 | 236 |