# bira2: Two-Level Blocked Individual-level Random Assignment Design In PowerUpR: Power Analysis Tools for Multilevel Randomized Experiments

## Description

For two-level randomized block designs (treatment at level 1, with random effects across level 2 blocks), use `mdes.bira2()` to calculate the minimum detectable effect size, `power.bira2()` to calculate the statistical power, and `mrss.bira2()` to calculate the minimum required sample size (number of blocks).

For treatment effect moderated by level 1 moderator use `power.mod211()`, `mdesd.mod211()`, and `mrss.mod211()` functions. For treatment effect moderated by level 2 moderator, use `power.mod212()`, `mdesd.mod212()`, and `mrss.mod212()` functions.

For partially nested blocked individual-level random assignment designs (blocked randomized controlled trial with intervention clusters) use `mdes.bira2_pn()` to calculate the minimum detectable effect size, `power.bira2_pn()` to calculate the statistical power, and `mrss.bira2_pn()` to calculate the minimum required sample size (number of blocks).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47``` ```mdes.bira2(power=.80, alpha=.05, two.tailed=TRUE, rel1=1, rho2, esv2=NULL, omega2=esv2/rho2, g2=0, r21=0, r2t2=0, p=.50, n, J) power.bira2(es=.25, alpha=.05, two.tailed=TRUE, rel1=1, rho2, esv2=NULL, omega2=esv2/rho2, g2=0, r21=0, r2t2=0, p=.50, n, J) mrss.bira2(es=.25, power=.80, alpha=.05, two.tailed=TRUE, rel1=1, rho2, esv2=NULL, omega2=esv2/rho2, r21=0, r2t2=0, J0=10, tol=.10, g2=0, p=.50, n) power.mod211(es=.25, alpha=.05, two.tailed=TRUE, rho2, omega2tm, r21=0, p=.50, q=NULL, n, J) mdesd.mod211(power=.80, alpha=.05, two.tailed=TRUE, rho2, omega2tm, g1=0, r21=0, p=.50, q=NULL, n, J) mrss.mod211(es=.25, power=.80, alpha=.05, two.tailed=TRUE, n, J0=10, tol=.10, rho2, omega2tm, r21=0, p=.50, q=NULL) power.mod212(es=.25, alpha=.05, two.tailed=TRUE, rho2, omega2t, r21=0, p=.50, q=NULL, n, J) mdesd.mod212(power=.80, alpha=.05, two.tailed=TRUE, rho2, omega2t, g1=0, r21=0, p=.50, q=NULL, n, J) mrss.mod212(es=.25, power=.80, alpha=.05, two.tailed=TRUE, n, J0=10, tol=.10, rho2, omega2t, r21=0, p=.50, q=NULL) mdes.bira2_pn(power=.80, alpha=.05, two.tailed=TRUE, df=NULL, rho2_trt=.20, omega2=.50, rho_ic=0, p=.50, g2=0, r21=0, n, J, ic_size=1) power.bira2_pn(es=.25,alpha=.05, two.tailed=TRUE, df=NULL, rho2_trt=.20, omega2=.50, rho_ic=0, p=.50, g2=0, r21=0, n, J, ic_size=1) mrss.bira2_pn(es=.25, power=.80, alpha=.05, two.tailed=TRUE, z.test=FALSE, rho2_trt=.20, omega2=.50, rho_ic=0, p=.50, g2=0, r21=0, n, ic_size=1, J0=10, tol=.10) ```

## 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. `df` degrees of freedom. `rho_ic` proportion of variance in the outcome (for treatment group) that is between intervention clusters. `rho2_trt` proportion of variance in the outcome (for treatment group) that is between level 2 units. `rel1` level 1 outcome reliability coefficient (see Cox \& Kelcey, 2019, p. 23). `rho2` proportion of variance in the outcome between level 2 units (unconditional ICC2). `rho` also works. `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). `esv` also works. Ignored when `omega2` is specified. `omega2` treatment effect heterogeneity as the ratio of the treatment effect variance between level 2 units to the unconditional level 2 residual variance. `omega` also works. `omega2t` standardized treatment effect variability across sites in the model that is not conditional on Level 2 moderator (ratio of the treatment effect variance between level 2 units to the total variance in the outcome.) `omega2tm` standardized effect variability of the moderation across sites (ratio of the moderated treatment effect variance between level 2 units to the total variance in the outcome.) `p` average proportion of level 1 units randomly assigned to treatment within level 2 units. `q` proportion of level 1 (on average) or level 2 units in the moderator subgroup. `g1` number of covariates at level 1. `g2` number of covariates at level 2. `r21` proportion of level 1 variance in the outcome explained by level 1 covariates (applies to all levels in partially nested designs). `r2t2` proportion of treatment effect variance among level 2 units explained by level 2 covariates. `n` level 1 sample size per block (average or harmonic mean). `J` number of blocks. `ic_size` sample size for each intervention cluster. `J0` starting value for `J`. `tol` tolerance to end iterative process for finding `J`. `z.test` logical; `TRUE` for z-test.

## 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. `J` number of level 2 units.

## References

Cox, K., \& Kelcey, B. (2019). Optimal design of cluster-and multisite-randomized studies using fallible outcome measures. Evaluation Review, 43(3-4), 189-225. doi: 10.1177/0193841X19870878

Dong, N., Kelcey, B., \& Spybrook, J. (2020). Design considerations in multisite randomized trials probing moderated treatment effects. Journal of Educational and Behavioral Statistics. Advance online publication. doi: 10.3102/1076998620961492

Dong, N., \& Maynard, R. (2013). PowerUp!: A tool for calculating minimum detectable effect sizes and minimum required sample sizes for experimental and quasi-experimental design studies. Journal of Research on Educational Effectiveness, 6(1), 24-67. doi: 10.1080/19345747.2012.673143

Lohr, S., Schochet, P. Z., \& Sanders, E. (2014). Partially nested randomized controlled trials in education research: A guide to design and analysis. NCER 2014-2000. National Center for Education Research. https://ies.ed.gov/ncer/pubs/20142000/pdf/20142000.pdf

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# cross-checks mdes.bira2(rho2=.17, omega2=.50, n=15, J=20) power.bira2(es=.366, rho2=.17, omega2=.50, n=15, J=20) mrss.bira2(es=.366, rho2=.17, omega2=.50, n=15) # cross-checks power.mod211(es=.248, rho2=.247, omega2tm=.148, r21=.493, n=20, J=35) mdes.mod211(power=.853, rho2=.247, omega2tm=.148, r21=.493, n=20, J=35) mrss.mod211(es=.248, power = .853, rho2=.247, omega2tm=.148, r21=.493, n=20) # cross-checks power.mod212(es=.248, rho2=.247, omega2t=.148, r21=.493, n=20, J=20) mdes.mod212(power=.739, rho2=.247, omega2t=.148, r21=.493, n=20, J=20) mrss.mod212(es=.248, power=.739, rho2=.247, omega2t=.148, r21=.493, n=20) # cross-checks mdes.bira2_pn(n=20, J=15, rho_ic=.10, ic_size=5) power.bira2_pn(es=.357, n=20, J=15, rho_ic=.10, ic_size=5) mrss.bira2_pn(es=.357, n=20, rho_ic=.10, ic_size=5) ```

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