cra2: Two-level Cluster-randomized Trials to Detect Main,...
In PowerUpR: Power Analysis Tools for Multilevel Randomized Experiments
Description
Usage
Arguments
Value
References
Examples
Description
For main treatment effects, use mdes.cra2() to calculate the minimum detectable effect size, power.cra2() to calculate the statistical power, mrss.cra2() to calculate the minimum required sample size (number of clusters).
For moderator at level 1, use mdesd.mod221() to calculate the minimum detectable effect size, power.mod221() to calculate the statistical power, mrss.mod221() to calculate the minimum required sample size (number of clusters).
For moderator at level 2, use mdesd.mod222() to calculate the minimum detectable effect size, power.mod222() to calculate the statistical power, mrss.mod222() to calculate the minimum required sample size (number of clusters).
For mediator at level 1 and level 2, use power.med211() to calculate the statistical power for the 2-1-1 mediation, and power.med221() for the 2-2-1 mediation.
For cluster-randomized block designs (treatment at level 2, with fixed effects across level 3 blocks), use mdes.bcra3f2() to calculate the minimum detectable effect size, power.bcra3f2() to calculate the statistical power, and mrss.bcra3f2() to calculate the minimum required sample size (number of clusters per block).
For partially nested cluster randomized trials (interventions clusters in treatment groups) use mdes.cra2_pn() to calculate the minimum detectable effect size, power.cra2_pn() to calculate the statistical power, and mrss.cra2_pn() to calculate the minimum required sample size (number of schools).
Usage
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mdes.cra2(power=.80, alpha=.05, two.tailed=TRUE,
rel1 = 1, rho2, p=.50, g2=0, r21=0, r22=0,
n, J)
mdesd.mod221(power=.80, alpha=.05, two.tailed=TRUE,
rho2, omegam2, r21=0, r2m2=0,
p=.50, q=NULL, n, J)
mdesd.mod222(power=.80, alpha=.05, two.tailed=TRUE,
rho2, r22=0,
p=.50, q=NULL, n, J)
power.cra2(es=.25, alpha=.05, two.tailed=TRUE,
rel1 = 1, rho2, g2=0, p=.50, r21=0, r22=0,
n, J)
power.mod221(es=.25, alpha=.05, two.tailed=TRUE,
rho2, omegam2, r21=0, r2m2=0,
p=.50, q=NULL, n, J)
power.mod222(es=.25, alpha=.05, two.tailed=TRUE,
rho2, r22=0,
p=.50, q=NULL, n, J)
power.med211(esa, esb1, esB, escp, two.tailed = TRUE, alpha = .05,
mc = FALSE, nsims = 1000, ndraws = 1000,
rhom2, rho2, r21, r22, r2m1, r2m2,
p, n, J)
power.med221(esa, esb, escp, two.tailed = TRUE, alpha = .05,
mc = FALSE, nsims = 1000, ndraws = 1000,
rho2, r22, r21, r2m2,
p = .50, n, J)
mrss.cra2(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
n, J0=10, tol=.10, rel1 = 1,
rho2, g2=0, p=.50, r21=0, r22=0)
mrss.mod221(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
n, J0=10, tol=.10, rho2, omegam2, r21=0, r2m2=0,
p=.50, q=NULL)
mrss.mod222(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
n, J0=10, tol=.10, rho2, r22=0,
p=.50, q=NULL)
mdes.bcra3f2(power=.80, alpha=.05, two.tailed=TRUE,
rho2, p=.50, g2=0, r21=0, r22=0,
n, J, K)
power.bcra3f2(es=.25, alpha=.05, two.tailed=TRUE,
rho2, p=.50, g2=0, r21=0, r22=0,
n, J, K)
mrss.bcra3f2(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
n, K, J0=10, tol=.10,
rho2, p=.50, g2=0, r21=0, r22=0)
mdes.cra2_pn(power=.80, alpha=.05, two.tailed=TRUE, df=NULL,
rho2_trt=.20, rho_ic=0, p=.50,
r21=0, n, J, ic_size=1)
power.cra2_pn(es=.25,alpha=.05, two.tailed=TRUE, df=NULL,
rho2_trt=.20, rho_ic=0, p=.50,
r21=0, n, J, ic_size=1)
mrss.cra2_pn(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
z.test=FALSE, rho2_trt=.20, rho_ic=0, p=.50,
r21=0, n, ic_size=1, J0=10, tol=.10)
Arguments
power
statistical power (1-β)
es, esa, esb, esb1, esB, escp
effect size for main/moderator effects, or for path coefficients a (treatment - mediator), b (level 2 mediator - outcome), b1 (level 1 mediator - outcome), B (overall mediator - outcome) or cp (direct treatment - outcome) in the mediation model.
alpha
probability of type I error.
two.tailed
logical; FALSE for one-tailed hypothesis testing.
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.
rel1
level 1 outcome reliability coefficient (Cox \& Kelcey, 2019b).
rho2
proportion of variance in the outcome between level 2 units (unconditional ICC2). rho also works.
rhom2
proportion of variance in the mediator between level 2 units.
omegam2
ratio of the unconditional variance in the moderator effect that is between level 2 units to the residual variance between level 2 units in the null model.
p
proportion of level 2 units randomly assigned to treatment.
q
proportion of level 1 or level 2 units in the moderator subgroup.
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).
r22
proportion of level 2 variance in the outcome explained by level 2 covariates.
r2m1
proportion of mediator variance at level 1 explained by level 1 covariates.
r2m2
proportion of variance in the moderator effect that is explained by level 2 predictors. For the mediation model, proportion of variance in the mediator explained by level 2 predictors.
n
harmonic mean of level 1 units across level 2 units (or simple average).
J
level 2 sample size.
K
number of level 3 units (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.
mc
logical; TRUE for monte carlo simulation based power.
nsims
number of replications, if mc = TRUE.
ndraws
number of draws from the distribution of the path coefficients for each replication, if mc = TRUE.
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. (2019a). Optimal sample allocation in group-randomized mediation studies with a group-level mediator. The Journal of Experimental Education, 87(4), 616-640. doi: 10.1080/00220973.2018.1496060
Cox, K., \& Kelcey, B. (2019b). 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., Spybrook J., Kelcey, B., \& Bulus, M. (2021). Power analyses for moderator effects with (non)random slopes in cluster randomized trials. Methodology, 17(2), 92-110. doi: 10.5964/meth.4003
Kelcey, B., Dong, N., Spybrook, J., \& Cox, K. (2017). Statistical power for causally defined indirect effects in group-randomized trials with individual-level mediators. Journal of Educational and Behavioral Statistics, 42(5), 499-530. doi: 10.3102/1076998617695506
Kelcey, B., Dong, N., Spybrook, J., \& Shen, Z. (2017). Experimental power for indirect effects in group-randomized studies with group-level mediators. Multivariate behavioral research, 52(6), 699-719. doi: 10.1080/00273171.2017.1356212
Kelcey, B., \& Shen, Z. (2020). Strategies for efficient experimental design in studies probing 2-1-1 mediation. The Journal of Experimental Education, 88(2), 311-334. doi: 10.1080/00220973.2018.1533796
Kelcey, B., Spybrook, J., \& Dong, N. (2019). Sample size planning for cluster-randomized interventions probing multilevel mediation. Prevention Science, 20(3), 407-418. doi: 10.1007/s11121-018-0921-6
Spybrook, J., Kelcey, B., \& Dong, N. (2016). Power for detecting treatment by moderator effects in two-and three-level cluster randomized trials. Journal of Educational and Behavioral Statistics, 41(6), 605-627. doi: 10.3102/1076998616655442
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
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# cross-checks for the main effect
mdes.cra2(rho2=.17, n=15, J=20)
power.cra2(es=.629, rho2=.17, n=15, J=20)
mrss.cra2(es=.629, rho2=.17, n=15)
# cross-checks for the randomly varying cont. L1 moderator effect
mdesd.mod221(rho2=.17, omegam2=.10, n=15, J=20)
power.mod221(es=.3563, rho2=.17, omegam2 =.10, n=15, J=20)
mrss.mod221(es=.3563, rho2=.17, omegam2 =.10, n=15)
# cross-checks for the non-randomly varying cont. L1 moderator effect
mdesd.mod221(rho2=.17, omegam2=0, n=15, J=20)
power.mod221(es=0.2957, rho2=.17, omegam2 =0, n=15, J=20)
mrss.mod221(es=0.2957, rho2=.17, omegam2 =0, n=15)
# cross-checks for the randomly varying bin. L1 moderator effect
mdesd.mod221(rho2=.17, omegam2=.10, q=.50, n=15, J=20)
power.mod221(es=.647, rho2=.17, omegam2 =.10, q=.50, n=15, J=20)
mrss.mod221(es=.647, rho2=.17, omegam2 =.10, q=.50, n=15)
# cross-checks for the non-randomly varying bin. L1 moderator effect
mdesd.mod221(rho2=.17, omegam2=0, q=.50, n=15, J=20)
power.mod221(es=0.5915, rho2=.17, omegam2 =0, q=.50, n=15, J=20)
mrss.mod221(es=0.5915, rho2=.17, omegam2 =0, q=.50, n=15)
# cross-checks for the cont. L2 moderator effect
mdesd.mod222(rho2=.17, n=15, J=100)
power.mod222(es=0.2757, rho2=.17, n=15, J=100)
mrss.mod222(es=0.2757, rho2=.17, n=15)
# cross-checks for the bin. L2 moderator effect
mdesd.mod222(rho2=.17, q=.50, n=15, J=100)
power.mod222(es=0.5514, rho2=.17, q=.50, n=15, J=100)
mrss.mod222(es=0.5514, rho2=.17, q=.50, n=15)
# 2-2-1 mediation
power.med221(esa=0.6596, esb=0.1891, escp=.1,
rho2=.15, r22=.52, r21=.40, r2m2=.50,
n=100, J=40, p=.5)
# 2-1-1 mediation
power.med211(esa=0.4135, esb1=0.0670, esB=0.3595, escp=.1,
rhom2=.3, rho2=.3, r22=.6, r21=.6, r2m2=.6, r2m1=.6,
n=30, J=80, p=.1)
# cross-checks for cluster-randomized block design
# treatment at level 2, with fixed effects across level 3 blocks
mdes.bcra3f2(rho2=.10, n=20, J=44, K=5)
power.bcra3f2(es = .145, rho2=.10, n=20, J=44, K=5)
mrss.bcra3f2(es = .145, rho2=.10, n=20, K=5)
# cross-checks for partially nested cluster-randomized trial
mdes.cra2_pn(n=40, J=70, rho2_trt=.15, rho_ic=.10, ic_size=10)
power.cra2_pn(es=.305, n=40, J=70, rho2_trt=.15, rho_ic=.10, ic_size=10)
mrss.cra2_pn(es=.305, n=40, rho2_trt=.15, rho_ic=.10, ic_size=10)
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Description Usage Arguments Value References Examples
Description
For main treatment effects, use mdes.cra2() to calculate the minimum detectable effect size, power.cra2() to calculate the statistical power, mrss.cra2() to calculate the minimum required sample size (number of clusters).
For moderator at level 1, use mdesd.mod221() to calculate the minimum detectable effect size, power.mod221() to calculate the statistical power, mrss.mod221() to calculate the minimum required sample size (number of clusters).
For moderator at level 2, use mdesd.mod222() to calculate the minimum detectable effect size, power.mod222() to calculate the statistical power, mrss.mod222() to calculate the minimum required sample size (number of clusters).
For mediator at level 1 and level 2, use power.med211() to calculate the statistical power for the 2-1-1 mediation, and power.med221() for the 2-2-1 mediation.
For cluster-randomized block designs (treatment at level 2, with fixed effects across level 3 blocks), use mdes.bcra3f2() to calculate the minimum detectable effect size, power.bcra3f2() to calculate the statistical power, and mrss.bcra3f2() to calculate the minimum required sample size (number of clusters per block).
For partially nested cluster randomized trials (interventions clusters in treatment groups) use mdes.cra2_pn() to calculate the minimum detectable effect size, power.cra2_pn() to calculate the statistical power, and mrss.cra2_pn() to calculate the minimum required sample size (number of schools).
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 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 | mdes.cra2(power=.80, alpha=.05, two.tailed=TRUE,
rel1 = 1, rho2, p=.50, g2=0, r21=0, r22=0,
n, J)
mdesd.mod221(power=.80, alpha=.05, two.tailed=TRUE,
rho2, omegam2, r21=0, r2m2=0,
p=.50, q=NULL, n, J)
mdesd.mod222(power=.80, alpha=.05, two.tailed=TRUE,
rho2, r22=0,
p=.50, q=NULL, n, J)
power.cra2(es=.25, alpha=.05, two.tailed=TRUE,
rel1 = 1, rho2, g2=0, p=.50, r21=0, r22=0,
n, J)
power.mod221(es=.25, alpha=.05, two.tailed=TRUE,
rho2, omegam2, r21=0, r2m2=0,
p=.50, q=NULL, n, J)
power.mod222(es=.25, alpha=.05, two.tailed=TRUE,
rho2, r22=0,
p=.50, q=NULL, n, J)
power.med211(esa, esb1, esB, escp, two.tailed = TRUE, alpha = .05,
mc = FALSE, nsims = 1000, ndraws = 1000,
rhom2, rho2, r21, r22, r2m1, r2m2,
p, n, J)
power.med221(esa, esb, escp, two.tailed = TRUE, alpha = .05,
mc = FALSE, nsims = 1000, ndraws = 1000,
rho2, r22, r21, r2m2,
p = .50, n, J)
mrss.cra2(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
n, J0=10, tol=.10, rel1 = 1,
rho2, g2=0, p=.50, r21=0, r22=0)
mrss.mod221(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
n, J0=10, tol=.10, rho2, omegam2, r21=0, r2m2=0,
p=.50, q=NULL)
mrss.mod222(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
n, J0=10, tol=.10, rho2, r22=0,
p=.50, q=NULL)
mdes.bcra3f2(power=.80, alpha=.05, two.tailed=TRUE,
rho2, p=.50, g2=0, r21=0, r22=0,
n, J, K)
power.bcra3f2(es=.25, alpha=.05, two.tailed=TRUE,
rho2, p=.50, g2=0, r21=0, r22=0,
n, J, K)
mrss.bcra3f2(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
n, K, J0=10, tol=.10,
rho2, p=.50, g2=0, r21=0, r22=0)
mdes.cra2_pn(power=.80, alpha=.05, two.tailed=TRUE, df=NULL,
rho2_trt=.20, rho_ic=0, p=.50,
r21=0, n, J, ic_size=1)
power.cra2_pn(es=.25,alpha=.05, two.tailed=TRUE, df=NULL,
rho2_trt=.20, rho_ic=0, p=.50,
r21=0, n, J, ic_size=1)
mrss.cra2_pn(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
z.test=FALSE, rho2_trt=.20, rho_ic=0, p=.50,
r21=0, n, ic_size=1, J0=10, tol=.10)
|
Arguments
power |
statistical power (1-β) |
es, esa, esb, esb1, esB, escp |
effect size for main/moderator effects, or for path coefficients a (treatment - mediator), b (level 2 mediator - outcome), b1 (level 1 mediator - outcome), B (overall mediator - outcome) or cp (direct treatment - outcome) in the mediation model. |
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. |
rel1 |
level 1 outcome reliability coefficient (Cox \& Kelcey, 2019b). |
rho2 |
proportion of variance in the outcome between level 2 units (unconditional ICC2). |
rhom2 |
proportion of variance in the mediator between level 2 units. |
omegam2 |
ratio of the unconditional variance in the moderator effect that is between level 2 units to the residual variance between level 2 units in the null model. |
p |
proportion of level 2 units randomly assigned to treatment. |
q |
proportion of level 1 or level 2 units in the moderator subgroup. |
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). |
r22 |
proportion of level 2 variance in the outcome explained by level 2 covariates. |
r2m1 |
proportion of mediator variance at level 1 explained by level 1 covariates. |
r2m2 |
proportion of variance in the moderator effect that is explained by level 2 predictors. For the mediation model, proportion of variance in the mediator explained by level 2 predictors. |
n |
harmonic mean of level 1 units across level 2 units (or simple average). |
J |
level 2 sample size. |
K |
number of level 3 units (blocks). |
ic_size |
sample size for each intervention cluster. |
J0 |
starting value for |
tol |
tolerance to end iterative process for finding |
z.test |
logical; |
mc |
logical; |
nsims |
number of replications, if |
ndraws |
number of draws from the distribution of the path coefficients for each replication, if |
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. (2019a). Optimal sample allocation in group-randomized mediation studies with a group-level mediator. The Journal of Experimental Education, 87(4), 616-640. doi: 10.1080/00220973.2018.1496060
Cox, K., \& Kelcey, B. (2019b). 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., Spybrook J., Kelcey, B., \& Bulus, M. (2021). Power analyses for moderator effects with (non)random slopes in cluster randomized trials. Methodology, 17(2), 92-110. doi: 10.5964/meth.4003
Kelcey, B., Dong, N., Spybrook, J., \& Cox, K. (2017). Statistical power for causally defined indirect effects in group-randomized trials with individual-level mediators. Journal of Educational and Behavioral Statistics, 42(5), 499-530. doi: 10.3102/1076998617695506
Kelcey, B., Dong, N., Spybrook, J., \& Shen, Z. (2017). Experimental power for indirect effects in group-randomized studies with group-level mediators. Multivariate behavioral research, 52(6), 699-719. doi: 10.1080/00273171.2017.1356212
Kelcey, B., \& Shen, Z. (2020). Strategies for efficient experimental design in studies probing 2-1-1 mediation. The Journal of Experimental Education, 88(2), 311-334. doi: 10.1080/00220973.2018.1533796
Kelcey, B., Spybrook, J., \& Dong, N. (2019). Sample size planning for cluster-randomized interventions probing multilevel mediation. Prevention Science, 20(3), 407-418. doi: 10.1007/s11121-018-0921-6
Spybrook, J., Kelcey, B., \& Dong, N. (2016). Power for detecting treatment by moderator effects in two-and three-level cluster randomized trials. Journal of Educational and Behavioral Statistics, 41(6), 605-627. doi: 10.3102/1076998616655442
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 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 48 49 50 51 52 53 54 55 | # cross-checks for the main effect
mdes.cra2(rho2=.17, n=15, J=20)
power.cra2(es=.629, rho2=.17, n=15, J=20)
mrss.cra2(es=.629, rho2=.17, n=15)
# cross-checks for the randomly varying cont. L1 moderator effect
mdesd.mod221(rho2=.17, omegam2=.10, n=15, J=20)
power.mod221(es=.3563, rho2=.17, omegam2 =.10, n=15, J=20)
mrss.mod221(es=.3563, rho2=.17, omegam2 =.10, n=15)
# cross-checks for the non-randomly varying cont. L1 moderator effect
mdesd.mod221(rho2=.17, omegam2=0, n=15, J=20)
power.mod221(es=0.2957, rho2=.17, omegam2 =0, n=15, J=20)
mrss.mod221(es=0.2957, rho2=.17, omegam2 =0, n=15)
# cross-checks for the randomly varying bin. L1 moderator effect
mdesd.mod221(rho2=.17, omegam2=.10, q=.50, n=15, J=20)
power.mod221(es=.647, rho2=.17, omegam2 =.10, q=.50, n=15, J=20)
mrss.mod221(es=.647, rho2=.17, omegam2 =.10, q=.50, n=15)
# cross-checks for the non-randomly varying bin. L1 moderator effect
mdesd.mod221(rho2=.17, omegam2=0, q=.50, n=15, J=20)
power.mod221(es=0.5915, rho2=.17, omegam2 =0, q=.50, n=15, J=20)
mrss.mod221(es=0.5915, rho2=.17, omegam2 =0, q=.50, n=15)
# cross-checks for the cont. L2 moderator effect
mdesd.mod222(rho2=.17, n=15, J=100)
power.mod222(es=0.2757, rho2=.17, n=15, J=100)
mrss.mod222(es=0.2757, rho2=.17, n=15)
# cross-checks for the bin. L2 moderator effect
mdesd.mod222(rho2=.17, q=.50, n=15, J=100)
power.mod222(es=0.5514, rho2=.17, q=.50, n=15, J=100)
mrss.mod222(es=0.5514, rho2=.17, q=.50, n=15)
# 2-2-1 mediation
power.med221(esa=0.6596, esb=0.1891, escp=.1,
rho2=.15, r22=.52, r21=.40, r2m2=.50,
n=100, J=40, p=.5)
# 2-1-1 mediation
power.med211(esa=0.4135, esb1=0.0670, esB=0.3595, escp=.1,
rhom2=.3, rho2=.3, r22=.6, r21=.6, r2m2=.6, r2m1=.6,
n=30, J=80, p=.1)
# cross-checks for cluster-randomized block design
# treatment at level 2, with fixed effects across level 3 blocks
mdes.bcra3f2(rho2=.10, n=20, J=44, K=5)
power.bcra3f2(es = .145, rho2=.10, n=20, J=44, K=5)
mrss.bcra3f2(es = .145, rho2=.10, n=20, K=5)
# cross-checks for partially nested cluster-randomized trial
mdes.cra2_pn(n=40, J=70, rho2_trt=.15, rho_ic=.10, ic_size=10)
power.cra2_pn(es=.305, n=40, J=70, rho2_trt=.15, rho_ic=.10, ic_size=10)
mrss.cra2_pn(es=.305, n=40, rho2_trt=.15, rho_ic=.10, ic_size=10)
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