Using this App

This Shiny app is for performing Monte Carlo simuations of factorial experimental designs in order to estimate power for an ANOVA and follow-up pairwise comparisons. This app allows you to violate the assumptions of homoscedascity and sphecity (for repeated measures). Also, the simulations take a considerable amount of time to run. If you don't need/want to violate these assumptions please use the ANOVA_exact app.
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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). Once you click Submit Design the design details will appear and you can continue onto the power analysis.

Power Simulation Tab

In this tab, you will setup the Monte Carlo simulation. You will have to specify a correction for multiple comparisons (default=none) and the alpha level (default=.05). If you have repeated measures you will need to specify the sphericity correction (default=none).

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 Power Shiny App
Option for estimated marginal means added
Now allows for unequal n input


Specify the factorial design below
*Must be specficied to continue*
Add numbers 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, or 'b' for between factors. Seperate factors with an 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).
Sample Size per Cell
Specify the list of standard deviations.
Specify the correlation matrix. If a correlation is entered across between subjects factor it will be reset to zero. Values only need to be entered in the upper triangular part and the app will take it from there.
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.
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 on the next tab.

Design Output

WARNING: Ensure sample sizes are the same between levels of within subjects factors (Otherwise the app will crash).

Simulate Power for Design

Simulation Parameters

Specify a seed number.
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