# bira4: Four-Level Blocked Individual-level Random Assignment Design In PowerUpR: Power Analysis Tools for Multilevel Randomized Experiments

## Description

For four-level randomized block designs (treatment at level 1, random effects across level 2, 3 and 4), use `mdes.bira4()` to calculate the minimum detectable effect size, `power.bira4()` to calculate the statistical power, and `mrss.bira4r1()` to calculate the minimum required sample size.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```mdes.bira4(power=.80, alpha=.05, two.tailed=TRUE, rho2, rho3, rho4, esv2=NULL, esv3=NULL, esv4=NULL, omega2=esv2/rho2, omega3=esv3/rho3, omega4=esv4/rho4, p=.50, r21=0, r2t2=0, r2t3=0, r2t4=0, g4=0, n, J, K, L) power.bira4(es=.25, alpha=.05, two.tailed=TRUE, rho2, rho3, rho4, esv2=NULL, esv3=NULL, esv4=NULL, omega2=esv2/rho2, omega3=esv3/rho3, omega4=esv4/rho4, p=.50, r21=0, r2t2=0, r2t3=0, r2t4=0, g4=0, n, J, K, L) mrss.bira4(es=.25, power=.80, alpha=.05, two.tailed=TRUE, n, J, K, L0=10, tol=.10, rho2, rho3, rho4, esv2=NULL, esv3=NULL, esv4=NULL, omega2=esv2/rho2, omega3=esv3/rho3, omega4=esv4/rho4, p=.50, r21=0, r2t2=0, r2t3=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). `esv2` effect size variability as the ratio of the treatment effect variance between level 2 units to the total variance in the outcome (level 1 + level 2 + level 3 + level 4). Ignored when `omega2` is specified. `esv3` effect size variability as the ratio of the treatment effect variance between level 3 units to the total variance in the outcome (level 1 + level 2 + level 3 + level 4). Ignored when `omega3` is specified. `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). Ignored when `omega4` is specified. `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. `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 1 units randomly assigned to treatment within level 2 units. `g4` number of covariates at level 4. `r21` proportion of level 1 variance in the outcome explained by level 1 covariates. `r2t2` proportion of treatment effect variance among level 2 units explained by level 2 covariates. `r2t3` proportion of treatment effect variance among level 3 units 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 8 9 10``` ```# cross-checks mdes.bira4(rho4=.05, rho3=.15, rho2=.15, omega4=.50, omega3=.50, omega2=.50, n=10, J=4, K=4, L=27) power.bira4(es = 0.142, rho4=.05, rho3=.15, rho2=.15, omega4=.50, omega3=.50, omega2=.50, n=10, J=4, K=4, L=27) mrss.bira4(es = 0.142, rho4=.05, rho3=.15, rho2=.15, omega4=.50, omega3=.50, omega2=.50, n=10, J=4, K=4) ```

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