# power.bira3r1: Model 2.4: Statistical Power Calculator for 3-Level Random... In PowerUpR: Power Analysis Tools for Multilevel Randomized Experiments

## Description

`power.bira3r1` calculates statistical power for designs with 3-levels where level 1 units are randomly assigned to treatment and control groups within level 2 units (random blocks).

## Usage

 ```1 2 3 4``` ``` power.bira3r1(mdes=.25, alpha=.05, two.tail=TRUE, rho2, rho3, omega2, omega3, P=.50, R12=0, RT22=0, RT32=0, g3=0, n, J, K, ...) ```

## Arguments

 `mdes` minimum detectable effect size. `alpha` probability of type I error. `two.tail` logical; `TRUE` for two-tailed hypothesis testing, `FALSE` for one-tailed hypothesis testing. `rho2` proportion of variance in the outcome explained by level 2 units. `rho3` proportion of variance in the outcome explained by level 3 units. `omega2` treatment effect heterogeneity as ratio of treatment effect variance among level 2 units to the residual variance at level 2. `omega3` treatment effect heterogeneity as ratio of treatment effect variance among level 3 units to the residual variance at level 3. `P` average proportion of level 1 units randomly assigned to treatment within level 2 units. `g3` number of covariates at level 3. `R12` proportion of level 1 variance in the outcome explained by level 1 covariates. `RT22` proportion of treatment effect variance among level 2 units explained by level 2 covariates. `RT32` proportion of treatment effect variance among level 3 units explained by level 3 covariates. `n` harmonic mean of level 1 units across level 2 units (or simple average). `J` harmonic mean of level 2 units across level 3 units (or simple average). `K` level 3 sample size. `...` to handle extra parameters passed from other functions, do not define any additional parameters.

## Details

Power formula was derived within power analysis framework descibed by Hedges & Rhoads (2009). Further definition of design parameters can be found in Dong & Maynard (2013).

## Value

 `fun` function name. `par` list of parameters used in power calculation. `df` degrees of freedom `M` multiplier for MDES calcuation given degrees of freedom, α and β (1-power). `power` statistical power (1 - type II error).

## Author(s)

Metin Bulus [email protected] Nianbo Dong [email protected]

## References

Dong, N., & Maynard, R. A. (2013). PowerUp!: A Tool for Calculating Minum Detectable Effect Sizes and Minimum Required Sample Sizes for Experimental and Quasi-Experimental Design Studies,Journal of Research on Educational Effectiveness, 6(1), 24-6.

Hedges, L. & Rhoads, C.(2009). Statistical Power Analysis in Education Research (NCSER 2010-3006). Washington, DC: National Center for Special Education Research, Institute of Education Sciences, U.S. Department of Education. This report is available on the IES website at http://ies.ed.gov/ncser/.

`mdes.bira3r1, mrss.bira3r1, optimal.bira3r1`
 ```1 2 3 4 5 6``` ```## Not run: power.bira3r1(rho3=.20, rho2=.15, omega3=.10, omega2=.10, n=69, J=10, K=100) ## End(Not run) ```