Model 3.2: MRSS Calculator for 3-Level Cluster Random Assignment Designs, Treatment at Level 3

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Description

mrss.cra3r3 calculates minimum required sample size for designs with 3-levels where level 3 units are randomly assigned to treatment and control groups.

Usage

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  mrss.cra3r3(mdes=.25, power=.80, alpha=.05, two.tail=TRUE,
              gm=2, ncase=10, constrain="power",
              n=NULL, J=NULL, K=NULL, K0=10, tol=.10,
              rho2, rho3,
              P=.50, g3=0, R12=0, R22=0, R32=0)

Arguments

mdes

minimum detectable effect size.

power

statistical power (1 - type II error).

alpha

probability of type I error.

two.tail

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

gm

grid multiplier to increase the range of sample size search for each level.

ncase

number of cases to show in the output.

constrain

parameter to contrain; "cost", "power", or "mdes".

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.

K0

starting value for estimating number of level 3 units.

tol

tolerance to stop the search algorithm.

rho2

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

rho3

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

P

proportion of level 3 units randomly assigned to treatment.

g3

number of covariates at level 3.

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.

Details

Level 3 sample size (K) is calculated using an iterative procedure described in Dong & Maynard (2013) due to model degrees of freedom dependency on K. For other levels (n, and J) MRSS calculation is simply solving for the unknown. MRSS calculator returns values that are not integer. Rounding may produce MDES and power values different from what was specified, therefore an integer solution is approximated using brute force (See Value section). Integer solution to MRSS for an omitted level assumes that specified sample sizes for remaining levels may subject to some changes.

Further definition of design parameters can be found in Dong & Maynard (2013).

Value

fun

function name.

par

list of parameters used in MRSS calculation.

round.mrss

solution after rounding.

integer.mrss

best integer solutions around round.mrss solution.

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.

See Also

mdes.cra3r3, power.cra3r3, optimal.cra3r3

Examples

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## Not run: 

     mrss.cra3r3(rho3=.06, rho2=.17,
                 n=15, J=3)

  
## End(Not run)

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