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CI for Poisson Rate

The CI for Poisson Rate uses the exact chi-squared method to calculate a confidence interval for the rate of occurrence of count data, such as defects per day or incidents per week.

Goal

Calculate a 95% confidence interval for the average defect rate from daily defect counts.

Sample Data

Press Copy for Excel, then paste the table into a blank worksheet.

Defects
3
1
4
2
5
0
3
2
4
1

Each row represents the number of defects observed on one day. Quantum XL will calculate the total occurrences, the observed rate, and the confidence interval around that rate.

Steps

1. Put the data in Excel

   Press Copy for Excel above the table, click cell A1 in a blank worksheet, and press Ctrl+V. The header row lands in row 1 and the 10 data rows in rows 2 through 11.

2. Launch the analysis

   From the Excel ribbon, select QXL Stat Tools → Analysis Tools → Confidence Interval → CI for Poisson Rate.

3. Select your data

   Select cells A1:A11 (the header row plus all 10 data rows).

4. Configure the analysis

   In the Confidence Interval dialog:

   • Data Columns: "Defects" should be checked
   • Confidence Level: 0.95 (default)

   Click Finish to generate the confidence interval.

Result

Quantum XL creates a whisker chart showing the 95% confidence interval for the Poisson rate. The statistics table shows:

• Sample Size: Number of observation periods (10 days)
• Total Occurrences: Sum of all defect counts (25)
• Rate of Occurrence: Average rate per period (2.5 defects per day)
• Lower Bound and Upper Bound: The 95% confidence interval for the true rate