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).
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)
statistical power \((1-\beta)\).
effect size.
probability of type I error.
logical; TRUE for two-tailed hypothesis testing, FALSE for one-tailed hypothesis testing.
degrees of freedom.
proportion of variance in the outcome (for treatment group) that is between intervention clusters.
proportion of variance in the outcome (for treatment group) that is between level 2 units.
level 1 outcome reliability coefficient (see Cox \& Kelcey, 2019, p. 23).
proportion of variance in the outcome between level 2 units (unconditional ICC2). rho also works.
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.
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.
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.)
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.)
average proportion of level 1 units randomly assigned to treatment within level 2 units.
proportion of level 1 (on average) or level 2 units in the moderator subgroup.
number of covariates at level 1.
number of covariates at level 2.
proportion of level 1 variance in the outcome explained by level 1 covariates (applies to all levels in partially nested designs).
proportion of treatment effect variance among level 2 units explained by level 2 covariates.
level 1 sample size per block (average or harmonic mean).
number of blocks.
sample size for each intervention cluster.
starting value for J.
tolerance to end iterative process for finding J.
logical; TRUE for z-test.
function name.
list of parameters used in power calculation.
degrees of freedom.
noncentrality parameter.
statistical power \((1-\beta)\).
minimum detectable effect size.
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. 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. 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. 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
# NOT RUN {
# 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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