How to calculate sample size with R applying mixed model design

Question

I would have a neuroimaging study (this possibly might be aside or help to figure out the problem). Participants are called to fill out a questionnaire, that turns a score in terms of technology usage. This would be used potentially as within-subjects variables, but this is not the case because I am to use it with no categorization in the model.

The outcome I am interested to use is the accuracy of each subject in a task where three task conditions are used. For each of these task conditions, two kinds of tasks exist (because they are essentially the same task with different kinds of stimuli to attend to). Thus, I assumed as my within-subjects variable with:

• Number of within-subjects variables (3 conditions) and for each variable, the number of levels of the variable (5/6 kinds of task because one of these is a repetition of the same task type, meaning the same task repeated twice. Thus, 5 should be the choice for me).

Now what I am asking is, in case I would model everything as

`Accuracy (dependent variable) in each Task Type(5/6)/ or Conditions (3)  ~ score*Task Conditions(3)/Task Type (5/6) or score + Task Conditions)/Task Type (5/6) + Gender 

Is the choice of a Manova study, like the following one, appropriate? How would you perform the calculation based on:

effect size f = 0.314 
power = 0.80 
alpha = 0.05

and no further parameters?

Which package/function would you recommend? Thanks

Answer 1

What you need might be the pwr package, which can do sample size and power calculations.

library(pwr)
pwr.anova.test(k=3,f = .314, power = 0.80, sig.level=0.05)

     Balanced one-way analysis of variance power calculation 

              k = 3
              n = 33.59194
              f = 0.314
      sig.level = 0.05
          power = 0.8

NOTE: n is number in each group