For four-level randomized block designs (treatment at level 1, random effects across level 2, 3 and 4), use mdes.bira4() to calculate the minimum detectable effect size, power.bira4() to calculate the statistical power, and mrss.bira4r1() to calculate the minimum required sample size.
mdes.bira4(power=.80, alpha=.05, two.tailed=TRUE,
rho2, rho3, rho4, esv2=NULL, esv3=NULL, esv4=NULL,
omega2=esv2/rho2, omega3=esv3/rho3, omega4=esv4/rho4,
p=.50, r21=0, r2t2=0, r2t3=0, r2t4=0, g4=0,
n, J, K, L)power.bira4(es=.25, alpha=.05, two.tailed=TRUE,
rho2, rho3, rho4, esv2=NULL, esv3=NULL, esv4=NULL,
omega2=esv2/rho2, omega3=esv3/rho3, omega4=esv4/rho4,
p=.50, r21=0, r2t2=0, r2t3=0, r2t4=0, g4=0,
n, J, K, L)
mrss.bira4(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
n, J, K, L0=10, tol=.10,
rho2, rho3, rho4, esv2=NULL, esv3=NULL, esv4=NULL,
omega2=esv2/rho2, omega3=esv3/rho3, omega4=esv4/rho4,
p=.50, r21=0, r2t2=0, r2t3=0, r2t4=0, g4=0)
statistical power \((1-\beta)\).
effect size.
probability of type I error.
logical; TRUE for two-tailed hypothesis testing, FALSE for one-tailed hypothesis testing.
proportion of variance in the outcome between level 2 units (unconditional ICC2).
proportion of variance in the outcome between level 3 units (unconditional ICC3).
proportion of variance in the outcome between level 4 units (unconditional ICC4).
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 + level 3 + level 4). Ignored when omega2 is specified.
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 + level 4). Ignored when omega3 is specified.
effect size variability as the ratio of the treatment effect variance between level 4 units to the total variance in the outcome (level 1 + level 2 + level 3 + level 4). Ignored when omega4 is specified.
treatment effect heterogeneity as ratio of treatment effect variance among level 2 units to the residual variance at level 2.
treatment effect heterogeneity as ratio of treatment effect variance among level 3 units to the residual variance at level 3.
treatment effect heterogeneity as ratio of treatment effect variance among level 4 units to the residual variance at level 4.
average proportion of level 1 units randomly assigned to treatment within level 2 units.
number of covariates at level 4.
proportion of level 1 variance in the outcome explained by level 1 covariates.
proportion of treatment effect variance among level 2 units explained by level 2 covariates.
proportion of treatment effect variance among level 3 units explained by level 3 covariates.
proportion of treatment effect variance among level 4 units explained by level 4 covariates.
harmonic mean of level 1 units across level 2 units (or simple average).
harmonic mean of level 2 units across level 3 units (or simple average).
harmonic mean of level 3 units across level 4 units (or simple average).
number of level 4 units.
starting value for L.
tolerance to end iterative process for finding L.
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 4 units.
# NOT RUN {
# cross-checks
mdes.bira4(rho4=.05, rho3=.15, rho2=.15,
omega4=.50, omega3=.50, omega2=.50,
n=10, J=4, K=4, L=27)
power.bira4(es = 0.142, rho4=.05, rho3=.15, rho2=.15,
omega4=.50, omega3=.50, omega2=.50,
n=10, J=4, K=4, L=27)
mrss.bira4(es = 0.142, rho4=.05, rho3=.15, rho2=.15,
omega4=.50, omega3=.50, omega2=.50,
n=10, J=4, K=4)
# }
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