bira4: Four-Level Blocked Individual-level Random Assignment Design

In PowerUpR: Power Analysis Tools for Multilevel Randomized Experiments

Description

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.

Usage

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)

Arguments

power	statistical power (1-β).
es	effect size.
alpha	probability of type I error.
two.tailed	logical; TRUE for two-tailed hypothesis testing, FALSE for one-tailed hypothesis testing.
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).
rho4	proportion of variance in the outcome between level 4 units (unconditional ICC4).
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 + level 3 + level 4). Ignored when omega2 is specified.
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 + level 4). Ignored when omega3 is specified.
esv4	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.
omega2	treatment effect heterogeneity as ratio of treatment effect variance among level 2 units to the residual variance at level 2.
omega3	treatment effect heterogeneity as ratio of treatment effect variance among level 3 units to the residual variance at level 3.
omega4	treatment effect heterogeneity as ratio of treatment effect variance among level 4 units to the residual variance at level 4.
p	average proportion of level 1 units randomly assigned to treatment within level 2 units.
g4	number of covariates at level 4.
r21	proportion of level 1 variance in the outcome explained by level 1 covariates.
r2t2	proportion of treatment effect variance among level 2 units explained by level 2 covariates.
r2t3	proportion of treatment effect variance among level 3 units explained by level 3 covariates.
r2t4	proportion of treatment effect variance among level 4 units explained by level 4 covariates.
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	harmonic mean of level 3 units across level 4 units (or simple average).
L	number of level 4 units.
L0	starting value for L.
tol	tolerance to end iterative process for finding L.

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.
L	number of level 4 units.

Examples

# 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)

PowerUpR documentation built on Oct. 25, 2021, 5:06 p.m.