Margin of Error for Two Independent Sample Means
Use the Margin of Error for Two Independent Sample Means Explorer to determine a sample size for a confidence interval. Select DOE > Sample Size Explorers > Confidence Intervals > Margin of Error for Two Independent Sample Means. Explore the trade offs between variability assumptions, sample size, significance, and the margin of error for your interval.
Interval Explorer for Two Independent Sample Means 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-sided 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.
Population Standard Deviation
Specifies the distribution for calculations.
Yes
Specifies known group standard deviations, calculations use the z distribution.
No
Specifies unknown group standard deviations, calculations use the t distribution.
Interval Explorer for Two Independent Sample Means 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 a standard deviation.
Margin of Error
Specifies the half-width of the 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. Select Lock to lock the Group 1 sample size.
Group 2 Sample Size
Specifies the number of observations (runs, experimental units, or samples) needed for Group 2 in your experiment. Select Lock to lock the Group 2 sample size.
Group 1 StdDev (σ1)
Specifies the assumed standard deviation for one of your groups, Group 1.
Group 2 StdDev (σ2)
Specifies the assumed standard deviation for the second group, 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 for Two Independent Sample Means 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.
Reset to Defaults
Resets all parameters and graphs to their default settings.
Help
Opens JMP online help.
Statistical Details for the Margin of Error for Two Independent Sample Means Explorer
The interval calculations for capturing the difference in population means is based on the standard normal or t distributions based on whether σ1 and σ2 are known or unknown.
The margin of error (MOE) is calculated as follows:
When σ1 and σ2 are unknown, the MOE is calculated as follows:
where
When σ is known, the MOE is calculated as follows:
where:
α is the significance level
z1-α is the (1 - α)th quantile of the normal distribution
t1-α,ν is the (1 - α)th quantile of the central t-distribution with ν degrees of freedom
n1 and n2 are the group sample sizes
σ1 and σ2 are the assumed group standard deviations.