ss.aipe.c.ancova {MBESS}

Sample size planning for a contrast in randomized ANCOVA from the Accuracy in Parameter Estimation (AIPE) perspective

Description

A function to calculate the appropriate sample size per group for the (unstandardized) contrast, in one-covariate randomized ANCOVA, so that the width of the confidence interval is sufficiently narrow.

Usage

ss.aipe.c.ancova(error.var.ancova = NULL, error.var.anova = NULL, 
rho = NULL, c.weights, width, conf.level = 0.95, 
assurance = NULL, certainty = NULL)

Arguments

error.var.ancova

the population error variance of the ANCOVA model (i.e., the mean square within of the ANCOVA model)

error.var.anova

the population error variance of the ANOVA model (i.e., the mean square within of the ANOVA model)

rho

the population correlation coefficient of the response and the covariate

c.weights

the contrast weights

width

the desired full width of the obtained confidence interval

conf.level

the desired confidence interval coverage, (i.e., 1 - Type I error rate)

assurance

parameter to ensure that the obtained confidence interval width is narrower than the desired width with a specified degree of certainty (must be NULL or between zero and unity)

certainty

an alias for assurance

Details

Either the error variance of the ANCOVA model or of the ANOVA model can be used to plan the appropriate sample size per group. When using the error variance of the ANOVA model to plan sample size, the correlation coefficient of the response and the covariate is also needed.

Value

n

the necessary sample size per group

Author(s)

Ken Kelley (University of Notre Dame; [e-mail]); Keke Lai <[e-mail]>

References

Kelley, K., Maxwell, S. E., & Rausch, J. R. (2003). Obtaining power or obtaining precision: Delineating methods of sample size planning. Evaluation and the Health Professions, 26, 258-287.

Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: A model comparison perspective. Mahwah, NJ: Erlbaum.

See Also

ci.c.ancova, ci.sc.ancova, ss.aipe.c

Examples

# Suppose the population error variance of some three-group ANOVA model
# is believed to be 40, and the population correlation coefficient 
# of the response and the covariate is 0.22. The researcher is 
# interested in the difference between the mean of group 1 and 
# the average of means of group 2 and 3. To plan the sample size so 
# that, with 90 percent certainty, the obtained 95 percent full 
# confidence interval width is no wider than 3:

ss.aipe.c.ancova(error.var.anova=40, rho=.22, 
c.weights=c(1, -0.5, -0.5), width=3, assurance=.90)