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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

Download ConfidenceInterval_Proportion.xlsx

Excel Protected View

When you open downloaded files, Excel displays a Protected View warning. You must click Enable Editing before you can use Quantum XL with the file.

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Alternatively, you can copy the sample data from the table below and paste it directly into a new Excel workbook.

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. Launch the analysis

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

  2. Select your data

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

  3. 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.