Model 2.4: Statistical Power Calculator for 3-Level Random Effects Blocked Individual Random Assignment Design, Individuals Randomized within Blocks

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Description

power.bira3r1 calculates statistical power for designs with 3-levels where level 1 units are randomly assigned to treatment and control groups within level 2 units (random blocks).

Usage

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  power.bira3r1(mdes=.25, alpha=.05, two.tail=TRUE,
               rho2, rho3, omega2, omega3,
               P=.50, R12=0, RT22=0, RT32=0, g3=0,
               n, J, K, ...)

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.

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.

P

average proportion of level 1 units randomly assigned to treatment within level 2 units.

g3

number of covariates at level 3.

R12

proportion of level 1 variance in the outcome explained by level 1 covariates.

RT22

proportion of treatment effect variance among level 2 units explained by level 2 covariates.

RT32

proportion of treatment effect variance among level 3 units explained by level 3 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

level 3 sample size.

...

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

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).

Value

fun

function name.

par

list of parameters used in power calculation.

df

model degrees of freedom

M

multiplier for MDES calcuation given model degrees of freedom, α and β (1-power).

power

statistical power (1 - type II error).

Author(s)

Metin Bulus bulus.metin@gmail.com Nianbo Dong dong.nianbo@gmail.com

References

Dong & Maynard (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.bira3r1, mrss.bira3r1, optimal.bira3r1

Examples

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## Not run: 

    power.bira3r1(rho3=.20, rho2=.15, omega3=.10, omega2=.10,
                 n=69, J=10, K=100)
  
## End(Not run)

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