Using this App

Please cite as: Lakens, D., & Caldwell, A. R. (2019). Simulation-Based Power-Analysis for Factorial ANOVA Designs.
This Shiny app is for performing 'exact' simuations of factorial experimental designs in order to estimate power for an ANOVA and follow-up pairwise comparisons. This app will not allow you to vary the standard deviations or the correlations in within-subjects designs. If you do need/want to violate these assumptions please use the ANOVA_power app.
Click here for the other app

The Design Tab

You must start with the Design tab in order to perform a power analysis. At this stage you must establish the parameters of the design (sample size, standard deviation, etc). *Please note the sample size must be greater than the product of the cells For example, 2b*2w = 4 and requires a sample size of at least 5 per cell. If this is entered incorrectly, then the 'Submit Design' button will be disabled. Once you click 'Submit Design' the design details will appear and you can continue onto the power analysis.

Exact Power Tab

In this tab, you will setup an *exact* simulation. All you can do at this stage is set the alpha level (default=.05) and decide the estimated marinal means analysis (optional)

Power curve Tab

In this tab, you can find your desired power (default = 90%) power across a range of sample sizes. All you need to do is set a minimum and maximum sample size. This tab will also allow you to download csv files including the power of ANOVA and estimated marginal means across a range of sample sizes.

Download your Simulation

Once your simulation is completed a button a button will appear on the sidebar to download a PDF


Current updates to Superpower's Exact Shiny App
Plot power now highlights the sample size at which desired power is achieved.

Design Input

Specify the factorial design below
*Must be specified to continue*
Add numbers for each factor that specify the number of levels in the factors (e.g., 2 for a factor with 2 levels). Add a 'w' after the number for within factors, and a 'b' for between factors. Seperate factors with a * (asterisks). Thus '2b*3w' is a design with two factors, the first of which has 2 between levels, and the second of which has 3 within levels.
Specify one word for each factor (e.g., AGE and SPEED) and the level of each factor (e.g., old and yound for a factor age with 2 levels).
Specify the correlation for within-subjects factors.
Note that for each cell in the design, a mean must be provided. Thus, for a '2b*3w' design, 6 means need to be entered. Means need to be entered in the correct order. The app provides a plot so you can check if you entered means correctly. The general principle has designated factors (i.e., AGE and SPEED) and levels (e.g., old, young).
Means for Each Cell in the Design
Click the button below to set up the design - Check the output to see if the design is as you intended, then you can run the simulation in the next tab.

Design Output


Exact Power for Design

Simulation Parameters

Keeping the default settings will result in all pairwise comparisons being performed.
The addition sign ('+') will add factors for comparisons while factors after a vertical bar '|' specifies the names of predictors to condition on
For more information on setting comparisons

Power Analysis Output

Find Desired Power Across a Range of Sample Sizes

Set Min and Max Sample Size

Enter Range of Sample Sizes

Note: No sphercity correction

Download Results for ANOVA and estimated marginal means
Download ANOVA Results


Estimated Marginal Means