Aim
Investigate the effect of Condition (0, 1, 2, 3) on Inclusion per Demographic participant group (0, 1, 2, 3) over Time (0, 1).
I have been looking for procedures to calculate the sample size I need to be able to get 80% power to find an effect size of at least 0.2 (small according to Cohen) before data collection.
Found procedure (formulas attached as pictures)
Using the book of Snijders and Bosker (1999) I found the following procedure:
1. Calculate Standard error (using Standard error calculation) with an effect size of 0.02 (small effect according to Cohen), an alpha of 0.05, and a power of .80. This lead to a standard error of 0.08.
2. Calculate n using the standard error from 1 (SE = .08), and assuming a standard deviation of 1 (and a mean of zero) under the normal distribution (using Standard error formula). This formula gives an n of 153.76.
3. Calculate the design effect (Design effect formula) with n = 153.76 and ρ = 0.08. This leads to a design effect of 13.22.
4. Multiplying n with the design effect in order to calculate the two-stage sample-size leads to a two-stage sample size of 2032
Questions
1. How can I know the intraclass correlation ρ before collecting data?
2. Why are there not parameters in the formulae about the amount of categories of my Condition, Demographic group, and Time variables?
3. Are there any easier procedures in order to calculate a sample size when using multilevel modeling?