Description Usage Arguments Value References Examples

For three-level cluster-randomized block designs (treatment at level 2, with random effects across level 3 blocks), use `mdes.bcra3r2()`

to calculate the minimum detectable effect size, `power.bcra3r2()`

to calculate the statistical power, and `mrss.bcra3r2()`

to calculate the minimum required sample size.

For partially nested blocked cluster randomized trials (interventions clusters in treatment groups) use `mdes.bcra3r2_pn()`

to calculate the minimum detectable effect size, `power.bcra3r2_pn()`

to calculate the statistical power, and `mrss.bcra3r2_pn()`

to calculate the minimum required sample size (number of blocks).

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 | ```
mdes.bcra3r2(power=.80, alpha=.05, two.tailed=TRUE,
rho2, rho3, esv3=NULL, omega3=esv3/rho3,
p=.50, g3=0, r21=0, r22=0, r2t3=0,
n, J, K)
power.bcra3r2(es=.25, alpha=.05, two.tailed=TRUE,
rho2, rho3, esv3=NULL, omega3=esv3/rho3,
p=.50, g3=0, r21=0, r22=0, r2t3=0,
n, J, K)
mrss.bcra3r2(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
n, J, K0=10, tol=.10,
rho2, rho3, esv3=NULL, omega3=esv3/rho3,
p=.50, g3=0, r21=0, r22=0, r2t3=0)
mdes.bcra3r2_pn(power=.80, alpha=.05, two.tailed=TRUE, df=NULL,
rho3_trt=.10, omega3=.50, rho2_trt=.20, rho_ic=0,
p=.50, r21=0, g3=0, n, J, K, ic_size=1)
power.bcra3r2_pn(es=.25,alpha=.05, two.tailed=TRUE, df=NULL,
rho3_trt=.10, omega3=.50, rho2_trt=.20, rho_ic=0,
p=.50, r21=0, g3=0, n, J, K, ic_size=1)
mrss.bcra3r2_pn(es=.25, power=.80, alpha=.05, two.tailed=TRUE, z.test=FALSE,
rho3_trt=.10, omega3 = .50, rho2_trt=.20, rho_ic=0,
p=.50, r21=0, g3=0, n, J, ic_size=1, K0=10, tol=.10)
``` |

`power` |
statistical power |

`es` |
effect size. |

`alpha` |
probability of type I error. |

`two.tailed` |
logical; |

`df` |
degrees of freedom. |

`rho_ic` |
proportion of variance in the outcome that is between intervention clusters. |

`rho2_trt` |
proportion of variance in the outcome (for treatment group) that is between level 2 units. |

`rho3_trt` |
proportion of variance in the outcome (for treatment group) that is between level 3 units. |

`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). |

`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). |

`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 2 units randomly assigned to treatment within level 3 units. |

`g3` |
number of covariates at level 3. |

`r21` |
proportion of level 1 variance in the outcome explained by level 1 covariates (applies to all levels in partially nested designs). |

`r22` |
proportion of level 2 variance in the outcome explained by level 2 covariates. |

`r2t3` |
proportion of treatment effect variance among level 3 units explained by level 3 covariates. |

`ic_size` |
sample size for each intervention cluster. |

`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` |
number of level 3 units. |

`K0` |
starting value for |

`tol` |
tolerance to end iterative process for finding |

`z.test` |
logical; |

`fun` |
function name. |

`parms` |
list of parameters used in power calculation. |

`df` |
degrees of freedom. |

`ncp` |
noncentrality parameter. |

`power` |
statistical power |

`mdes` |
minimum detectable effect size. |

`K` |
number of level 3 units. |

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# cross-checks
mdes.bcra3r2(rho3=.13, rho2=.10, omega3=.4,
n=10, J=6, K=24)
power.bcra3r2(es = .246, rho3=.13, rho2=.10, omega3=.4,
n=10, J=6, K=24)
mrss.bcra3r2(es = .246, rho3=.13, rho2=.10, omega3=.4,
n=10, J=6)
# cross-checks
mdes.bcra3r2_pn(rho3_trt=.10, omega3=.50,
rho2_trt=.15, rho_ic=.20,
n=40, J=60, K=6, ic_size=10)
power.bcra3r2_pn(es=.399, rho3_trt=.10, omega3=.50,
rho2_trt=.15, rho_ic=.20,
n=40, J=60, K=6, ic_size=10)
mrss.bcra3r2_pn(es=.399, rho3_trt=.10, omega3=.50,
rho2_trt=.15, rho_ic=.20,
n=40, J=60, ic_size=10)
``` |

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