Home / Statistical Tools / Analysis Tools / Confidence Interval / How-To / CI for Binomial Proportion

CI for Binomial Proportion

The CI for Binomial Proportion uses the Clopper-Pearson exact method (via the Beta distribution) to calculate confidence intervals for binary outcome data. Your data must have exactly 2 unique values (e.g., Pass/Fail, Yes/No, Defective/Good).

Goal

Calculate a 95% confidence interval for the Pass and Fail proportions from inspection data.

Sample Data

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

Result
Pass
Pass
Fail
Pass
Pass
Pass
Fail
Pass
Pass
Fail

Each row represents one inspection result. There are 7 Pass and 3 Fail outcomes out of 10 observations.

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 Binomial Proportion.

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: "Result" should be checked
   • Confidence Level: 0.95 (default)

   Click Finish to generate the confidence interval.

Result

Quantum XL creates two whisker groups for the Result column, one for Pass and one for Fail. The statistics table shows:

• Sample Size: Total observations (10)
• Pass: Count (7), proportion (0.70), lower and upper bounds
• Fail: Count (3), proportion (0.30), lower and upper bounds

The Clopper-Pearson exact method is used, which provides conservative (wider) intervals compared to the normal approximation.

Exactly 2 Unique Values Required

Binomial Proportion CI requires exactly 2 unique values in your data. If the column has fewer than 2 or more than 2 unique values, the analysis will show "requires 2 unique values" instead of producing a confidence interval.