Description Usage Arguments Value References Examples

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).

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)
``` |

`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 (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). |

`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). |

`omega2` |
treatment effect heterogeneity as the ratio of the treatment effect variance between level 2 units to the unconditional level 2 residual variance. |

`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 |

`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. |

`J` |
number of level 2 units. |

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

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)
``` |

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