Planning for precise contrasts in two-way factorial designs: a Tutorial

I've created a first version of Shiny App for sample size planning for precise contrast estimates in one and two-way designs. So, if you want to plan for interaction contrasts for two-way designs, take a look here: https://gmulder.shinyapps.io/PlanningFactorialContrasts/

Important: this is a first version that contains no error checking (but you know what you're doing, so that's not a problem). Also, I have not tested the results of the app with simulation studies. As soon as I have done that, I will share the code of the app.


Update: The values for the factorial two-way within subjects designs are checked with simulation studies (for f = .40, assurance = .80, and correlation rho = .50).

Note: if you have a single factor design, you may also consider looking here: https://the-small-s-scientist.blogspot.com/2018/11/contrast-tutorial.html

Note: if you have a two-groups independent design, go here for an introduction to sample size planning and its relation to the power of the t-test: https://the-small-s-scientist.blogspot.com/2018/03/sample-size-planning-shiny-app.html

See for more detailed information about sample size planning for single factor and factorial designs (between, within, and mixed): https://the-small-s-scientist.blogspot.com/2019/04/sample-size-planning-for-contrast-estimates.html and for guidelines for setting target MoE: https://the-small-s-scientist.blogspot.com/2019/03/planning-with-assurance-with-assurance.html)

How does the app work?

1. Specifying Target MoE and Assurance 

Target MoE should be specified in a number of standard deviations (usually a fraction; for details see Cumming, 2012; Cumming & Calin-Jageman, 2017). The symbol f will be used to refer to this standardized MoE. Target MoE (f) must be larger than zero (f will be automatically set to .05 if you accidentally fill in the value 0). 

I suggest using the following guidelines for target MoE (f): 

Description	f
Extremely Precise	.05
Very Precise	.10
Precise	.25
Reasonably Precise	.40
Borderline Precise	.65

You should only use these guidelines if you lack the information you need for specifying a reasonable value for Target MoE.

Assurance is the probability that (to be) obtained MoE will be no larger than Target MoE. I suggest setting Assurance minimally at .80.

Planning for Precise Contrasts: Tutorial for single factor designs

This is a tutorial for  a planning for precision  of contrasts estimates. The application is here: https://gmulder.shinyapps.io/PlanningContrasts/.

NOTE: For a (beta) version of planning for factoral designs: https://the-small-s-scientist.blogspot.com/2018/11/contrasts-factorial-tutorial.html

NOTE: I've updated the app with a few corrections, so there is a new version. (The November version has corrected degrees of freedom  for the 3 and 4 condition within design).

If you like to run the app in R, install the shiny and devtool packages and run the following:

library(shiny)
library(devtools)

source_url("https://git.io/fpI1R")

shinyApp(ui = ui, server = server)

Specifying Target MoE and Assurance 

Target MoE should be specified in a number of standard deviations (usually a fraction; for details see Cumming, 2012; Cumming & Calin-Jageman, 2017). The symbol f will be used to refer to this standardized MoE. Target MoE (f) must be larger than zero (f will be automatically set to .05 if you accidentally fill in the value 0). 

I suggest using the following guidelines for target MoE (f): 

Description	f
Extremely Precise	.05
Very Precise	.10
Precise	.25
Reasonably Precise	.40
Borderline Precise	.65

You should only use these guidelines if you lack the information you need for specifying a reasonable value for Target MoE.

Assurance is the probability that (to be) obtained MoE will be no larger than Target MoE. I suggest setting Assurance minimally at .80. 

Specifying the Design

The app works with independent and dependent designs for 2, 3, and 4 conditions.  With 2 conditions, the analysis is equivalent to the independent and dependent t-tests, with more than two conditions the analysis is equivalent to one-way independent ANOVA or dependent ANOVA.


Specifying the Cross-Condition correlation
If you choose the dependent design, you also need to specify a value for the cross-condition correlation. This value should be larger than zero. One of the assumptions underlying the app, is that there is only 1 observation per participant (or any other unit of analysis). That is why I like to think of this correlation as (conceptually related to) the reliability of the participant scores (averaged over conditions). From that perspective, a correlation around .60 would be borderline acceptable and around .80 would be considered good enough. So, for worst-case scenarios use a correlation smaller than .60, and for optimistic scenario's correlations of .80 or larger.

Note: for technical reasons a correlation of 1 will be automatically changed to .99.

For independent designs the correlation should equal 0. (And the above story about reliability does no longer make sense; but we also do not need it).