bcra3r2 {PowerUpR}

Three-Level Blocked Cluster-level Random Assignment Design, Treatment at Level 2

Description

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).

Usage

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)

Arguments

power

statistical power (1-\beta).

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 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). esv also works. Ignored when omega3 is specified.

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 K.

tol

tolerance to end iterative process for finding K.

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-\beta).

mdes

minimum detectable effect size.

K

number of level 3 units.

References

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

# 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)