Power for ANOVA
Use the Power for ANOVA Explorer to determine a sample size for a study of k groups or treatments to be analyzed using ANOVA. Select DOE > Sample Size Explorers > Power > Power for ANOVA. Explore the trade offs between variability assumptions, sample size, power and significance. Sample size and power are associated with the following hypothesis test:
versus the two-sided alternative:
where:
Power Explorer for ANOVA Options
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.
Test Specification
Options to specify what quantity you make assumptions about.
Group Means
Specify the group means, assume equal group variances.
Between-group Variance
Specify the between-group variance, assume equal group variances.
Maximum Difference
Specify the maximum difference in means to detect.
Worst Case
Specify the maximum difference between the largest and smallest mean, assuming that all other means are equal.
All but One
Specify the maximum difference between the largest or smallest mean, assuming that all other means are equal.
Preliminary Information
Alpha
Specifies the probability of a type I error, which is the probability of rejecting the null hypothesis when it is true. It is commonly referred to as the significance level of the test. The default alpha level is 0.05.
Number of groups
Specifies the number of groups or treatments in your experiment.
Power Explorer for ANOVA Profiler
The profiler enables you to visualize the impact of sample size assumptions on the power calculations.
Solve for
Enables you to solve for a sample size, within group standard deviation, or maximum difference in means.
Power
Specifies the probability of rejecting the null hypothesis when it is false. With all other parameters fixed, power increases as sample size increases.
Sample size (per group)
Specifies the number of observations (runs, experimental units, or treatments) needed for each group in your experiment.
Note: Only equal group sample sizes supported.
Within-group variance (σ2)
Specifies the assumed population variance for each group where the standard deviation is assumed to be equal across groups.
Group Mean
(Available only for Test Specification set to Group means.) Specifies the assumed group mean. There is one profiler and text box for each group specified in the preliminary information.
Between-group variance
(Available only for Test Specification set to Between-group variance.) Specifies the variance of the individual group means around the grand mean. This is the sum of the squared differences between the group means and the grand mean scaled by 1/(K-1) for K groups.
Maximum Difference in Means
(Available only for Test Specification set to Maximum Difference.) Specifies the maximum difference between the most extreme mean and all other means (all but one) or the maximum difference between the two most extreme means (worst case).
Power Explorer for ANOVA 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 Power for ANOVA Explorer
The power calculations for testing differences among means from multiple groups assumes equal standard deviations for each group. Power calculations are based on the standard F test. The power (1-β) is computed based on the test specification.
For group means:
For between-groups:
For maximum difference, worst case:
For maximum difference, all but one:
where
F(q, df1, df2, λ) is a non-central F-distribution with noncentrality parameter λ.
K is the number of groups
n is the number of samples within each group (assumed equal for all groups)
N = nK
μk is the assumed mean for group k
σ2BG is the sum of the squared differences between the group means and the grand mean scaled by 1/(K-1)
δWC is the difference between the largest and smallest group means
δABO is the difference between one mean and the average of all other means
σ2 is the within-group variance (assumed equal for all groups)