bcra4r3 function

Four-Level Blocked Cluster-level Random Assignment Design, Treatment at Level 3

For four-level cluster-randomized block designs (treatment at level 3, with random effects across level 4 blocks), use mdes.bcra4r3() to calculate the minimum detectable effect size, power.bcra4r3() to calculate the statistical power, and mrss.bcra4r3() to calculate the minimum required sample size.

mdes.bcra4r3(power=.80, alpha=.05, two.tailed=TRUE,
             rho2, rho3, rho4, esv4=NULL, omega4=esv4/rho4,
             p=.50, r21=0, r22=0, r23=0, r2t4=0, g4=0,
             n, J, K, L)

power.bcra4r3(es=.25, alpha=.05, two.tailed=TRUE,
              rho2, rho3, rho4, esv4=NULL, omega4=esv4/rho4,
              p=.50, r21=0, r22=0, r23=0, r2t4=0, g4=0,
              n, J, K, L)

mrss.bcra4r3(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
             n, J, K, L0=10, tol=.10,
             rho2, rho3, rho4, esv4=NULL, omega4=esv4/rho4,
             p=.50, r21=0, r22=0, r23=0, r2t4=0, g4=0)

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.
• 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).
• 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). esv also works. Ignored when omega4 is specified.
• 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 3 units randomly assigned to treatment within level 4 units.
• g4: number of covariates at level 4.
• r21: proportion of level 1 variance in the outcome explained by level 1 covariates.
• r22: proportion of level 2 variance in the outcome explained by level 2 covariates.
• r23: proportion of level 3 variance in the outcome 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.

Returns

• 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.

• L: number of level 4 units.

Examples

# cross-checks
mdes.bcra4r3(rho4=.05, rho3=.15, rho2=.15,
             omega4=.50, n=10, J=4, K=4, L=20)
power.bcra4r3(es = .316, rho4=.05, rho3=.15, rho2=.15,
              omega4=.50, n=10, J=4, K=4, L=20)
mrss.bcra4r3(es = .316, rho4=.05, rho3=.15, rho2=.15,
             omega4=.50, n=10, J=4, K=4)