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Design of Experiments Guide > Sample Size Explorers > Confidence Interval Explorers > Margin of Error for Two Independent Sample Proportions
Publication date: 06/21/2023

Margin of Error for Two Independent Sample Proportions

Use the Margin of Error for Two Independent Sample Proportions Explorer to determine a sample size for a confidence interval for the difference in two proportions, for log relative risk, or for log odds. Select DOE > Sample Size Explorers > Confidence Intervals > Margin of Error for Two Independent Sample Proportions. Explore the trade offs between variability assumptions, sample size, significance, and the margin of error for your interval.

Interval Explorer Two Independent Sample Proportions 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 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.

Difference in Proportions

Specifies a confidence interval for the difference in two proportions (p1 - p2).

Log Relative Risk

Specifies a confidence interval for the relative risk (p1/p2) on a log scale.

Log Odds

Specifies a confidence interval for the odds (p1/(1-p2)) on a log scale.

Interval Explorer Two Independent Sample Proportions Profiler

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

Total Sample Size

Specifies the total number of observations (runs, experimental units, or samples) needed for your experiment. The margin of error curve is based on total sample size. Select Lock to lock the total sample size.

Solve for

Enables you to solve for a sample size or an assumed proportion.

Margin of Error

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

Group 1 Sample Size

Specifies the number of observations (runs, experimental units, or samples) needed for Group 1 in your experiment.

Group 2 Sample Size

Specifies the number of observations (runs, experimental units, or samples) needed for Group 2 in your experiment.

Group 1 Proportion

Specifies the assumed proportion for Group 1.

Group 2 Proportion

Specifies the assumed proportion for Group 2.

Note: Adjusting the sample size for one group adjusts the total sample size unless the total sample size is locked. In that case, adjusting the sample size for one group adjust the sample size for the second group.

Interval Explorer Two Independent Sample Proportions 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 Margin of Error for Two Independent Sample Proportions Explorer

The calculations for each interval type are based on normal approximations.

Difference in Proportions

For intervals about the difference in proportions the margin of error (MOE) is calculated as follows:

Equation shown here

The bounds are calculated as follows:

Equation shown here

Log Relative Risk

For the logarithm of the relative risk the margin of error (MOE) is calculated as follows:

Equation shown here

The bounds are calculated as follows:

Equation shown here

Log Odds

For the logarithm of the odds ratio, the margin of error is calculated as follows:

Equation shown here

The bounds are calculated as follows:

Equation shown here

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