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Publication date: 04/21/2023

Margin of Error for One Sample Proportion

Use the Margin of Error for One Sample Proportion to determine a sample size for a confidence interval. Select DOE > Sample Size Explorers > Confidence Intervals > Margin of Error for One Sample Proportion. Explore the trade offs between the assumed proportion, sample size, significance, and the margin of error for your interval. Calculations use score confidence intervals.

Interval Explorer for One Sample Proportion Settings

Set study assumptions and explore sample sizes using the radio buttons, text boxes, and menus. The profiler updates as you make changes to the settings. Alternatively, change settings by dragging the cross hairs on the profiler curves.

Interval Type

One-sided

Specifies a one-side of the interval (upper or lower bound)

Two-sided

Specifies a two-sided interval.

Preliminary Information

Alpha

Specifies the confidence level, 1 - Alpha. The default alpha level is 0.05 for a 95% confidence interval.

Interval Explorer for One Sample Proportion Profiler

The profiler enables you to visualize the impact of sample size assumptions on the margin of error calculations.

Solve for

Enables you to solve for the sample size or assumed proportion.

Margin of Error

Specifies the half-width of the interval. With all other parameters fixed, margin of error decreases as sample size increases.

Sample Size

Specifies the total number of observations (runs, experimental units, or samples) needed to construct your interval.

Proportion

Specifies the assumed proportion for the interval.

Interval Explorer for One Sample Proportion Options

The Explorer red triangle menu and report buttons provide additional options:

Simulate Data

Opens a data table of simulated data based on the explorer settings. View the simulated response column formula for the settings used.

Make Data Collection Table

Creates a new data table that you can use for data collection. The table includes scripts to facilitate data analysis.

Save Settings

Saves the current settings to the Saved Settings table. This enables you to save a set of alternative study plans. See Saved Settings in the Sample Size Explorers.

Help

Opens JMP help.

Statistical Details for the One Sample Proportion Interval Explorer

The interval calculations for capturing a population proportion is based on the Agresti-Coull method, see Agresti and Coull(1998). This method is also known as score confidence intervals.

The margin of error (MOE) for confidence intervals is calculated as follows:

Equation shown here

The bound is calculated as follows:

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where

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and

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and q = 1 - α/2 for an interval or q = 1 - α for a bound.

Want more information? Have questions? Get answers in the JMP User Community (community.jmp.com).