# bcra4r3: Four-Level Blocked Cluster-level Random Assignment Design,... In PowerUpR: Power Analysis Tools for Multilevel Randomized Experiments

## Description

For four-level cluster-randomized block designs (treatment at level 3, with random effects across level 4 blocks), use `mdes.bcra4r3()` to calculate the minimum detectable effect size, `power.bcra4r3()` to calculate the statistical power, and `mrss.bcra4r3()` to calculate the minimum required sample size.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```mdes.bcra4r3(power=.80, alpha=.05, two.tailed=TRUE, rho2, rho3, rho4, esv4=NULL, omega4=esv4/rho4, p=.50, r21=0, r22=0, r23=0, r2t4=0, g4=0, n, J, K, L) power.bcra4r3(es=.25, alpha=.05, two.tailed=TRUE, rho2, rho3, rho4, esv4=NULL, omega4=esv4/rho4, p=.50, r21=0, r22=0, r23=0, r2t4=0, g4=0, n, J, K, L) mrss.bcra4r3(es=.25, power=.80, alpha=.05, two.tailed=TRUE, n, J, K, L0=10, tol=.10, rho2, rho3, rho4, esv4=NULL, omega4=esv4/rho4, p=.50, r21=0, r22=0, r23=0, r2t4=0, g4=0) ```

## Arguments

 `power` statistical power (1-β). `es` effect size. `alpha` probability of type I error. `two.tailed` logical; `TRUE` for two-tailed hypothesis testing, `FALSE` for one-tailed hypothesis testing. `rho2` proportion of variance in the outcome between level 2 units (unconditional ICC2). `rho3` proportion of variance in the outcome between level 3 units (unconditional ICC3). `rho4` proportion of variance in the outcome between level 4 units (unconditional ICC4). `esv4` effect size variability as the ratio of the treatment effect variance between level 4 units to the total variance in the outcome (level 1 + level 2 + level 3 + level 4). `esv` also works. Ignored when `omega4` is specified. `omega4` treatment effect heterogeneity as ratio of treatment effect variance among level 4 units to the residual variance at level 4. `p` average proportion of level 3 units randomly assigned to treatment within level 4 units. `g4` number of covariates at level 4. `r21` proportion of level 1 variance in the outcome explained by level 1 covariates. `r22` proportion of level 2 variance in the outcome explained by level 2 covariates. `r23` proportion of level 3 variance in the outcome explained by level 3 covariates. `r2t4` proportion of treatment effect variance among level 4 units explained by level 4 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` harmonic mean of level 3 units across level 4 units (or simple average). `L` number of level 4 units. `L0` starting value for `L`. `tol` tolerance to end iterative process for finding `L`.

## Value

 `fun` function name. `parms` list of parameters used in power calculation. `df` degrees of freedom. `ncp` noncentrality parameter. `power` statistical power (1-β). `mdes` minimum detectable effect size. `L` number of level 4 units.

## Examples

 ```1 2 3 4 5 6 7``` ```# cross-checks mdes.bcra4r3(rho4=.05, rho3=.15, rho2=.15, omega4=.50, n=10, J=4, K=4, L=20) power.bcra4r3(es = .316, rho4=.05, rho3=.15, rho2=.15, omega4=.50, n=10, J=4, K=4, L=20) mrss.bcra4r3(es = .316, rho4=.05, rho3=.15, rho2=.15, omega4=.50, n=10, J=4, K=4) ```

PowerUpR documentation built on Oct. 25, 2021, 5:06 p.m.