PowerUpR (version 0.1.3)

power.bcra4r3: Model 4.5: Statistical Power Calculator for 4-Level Random Effects Blocked Cluster Random Assignment Designs, Treatment at Level 3

Description

power.bcra4r3 calculates statistical power for designs with 4-levels where level 3 units are randomly assigned to treatment and control groups within level 4 units (random blocks).

Usage

power.bcra4r3(mdes=.25, alpha=.05, two.tail=TRUE,
       rho2, rho3, rho4, omega4,
       P=.50, R12=0, R22=0, R32=0, RT42=0, g4=0,
       n, J, K, L, ...)

Arguments

mdes

minimum detectable effect size.

alpha

probability of type I error.

two.tail

logical; TRUE for two-tailed hypothesis testing, FALSE for one-tailed hypothesis testing.

rho2

proportion of variance in the outcome explained by level 2 units.

rho3

proportion of variance in the outcome explained by level 3 units.

rho4

proportion of variance in the outcome explained by level 4 units.

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.

R12

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.

R32

proportion of level 3 variance in the outcome explained by level 3 covariates.

RT42

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.

...

to handle extra parameters passed from other functions, do not define any additional parameters.

Value

fun

function name.

par

list of parameters used in power calculation.

df

degrees of freedom

M

multiplier for MDES calcuation given degrees of freedom, \(\alpha\) and \(\beta\) (1-power).

power

statistical power (1 - type II error).

Details

Power formula was derived within power analysis framework descibed by Hedges & Rhoads (2009). Further definition of design parameters can be found in Dong & Maynard (2013) and Hedges & Rhoads (2009).

References

Dong, N., & Maynard, R. A. (2013). PowerUp!: A Tool for Calculating Minum Detectable Effect Sizes and Minimum Required Sample Sizes for Experimental and Quasi-Experimental Design Studies,Journal of Research on Educational Effectiveness, 6(1), 24-6. Hedges, L. & Rhoads, C.(2009). Statistical Power Analysis in Education Research (NCSER 2010-3006). Washington, DC: National Center for Special Education Research, Institute of Education Sciences, U.S. Department of Education. This report is available on the IES website at http://ies.ed.gov/ncser/.

See Also

mdes.bcra4r3, mrss.bcra4r3, optimal.bcra4r3

Examples

## Not run: ------------------------------------
# 
#     power.bcra4r3(rho4=.05, rho3=.15, rho2=.15,
#                  omega4=.50,
#                  n=10, J=4, L=27, K=4)
#   
## ---------------------------------------------