Sample size planning from the AIPE perspective for standardized ANCOVA contrasts

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Description

Sample size planning from the accuracy in parameter estimation (AIPE) perspective for standardized ANCOVA contrasts.

Usage

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ss.aipe.sc.ancova(Psi = NULL, sigma.anova = NULL, sigma.ancova = NULL,
psi = NULL, ratio = NULL, rho = NULL, divisor = "s.ancova", 
c.weights, width, conf.level = 0.95, assurance = NULL, ...)

Arguments

Psi

the population unstandardized ANCOVA (adjusted) contrast

sigma.anova

the population error standard deviation of the ANOVA model

sigma.ancova

the population error standard deviation of the ANCOVA model

psi

the population standardized ANCOVA (adjusted) contrast

ratio

the ratio of sigma.ancova over sigma.anova

rho

the population correlation coefficient between the response and the covariate

divisor

which error standard deviation to be used in standardizing the contrast; the value can be either "s.ancova" or "s.anova"

c.weights

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)

...

allows one to potentially include parameter values for inner functions

Details

The sample size planning method this function is based on is developed in the context of simple (i.e., one-response-one-covariate) ANCOVA model and randomized design (i.e., same population covariate mean across groups).

An ANCOVA contrast can be standardized in at least two ways: (a) divided by the error standard deviation of the ANOVA model, (b) divided by the error standard deviation of the ANCOVA model. This function can be used to analyze both types of standardized ANCOVA contrasts.

Not all of the arguments about the effect sizes need to be specified. If divisor="s.ancova" is used in the argument, then input either (a) psi, or (b) Psi and s.ancova. If divisor="s.anova" is used in the argument, possible specifications are (a) Psi, s.ancova, and s.anova; (b) psi, and ratio; (c) psi, and rho.

Value

This function returns the sample size per group.

Note

When divisor="s.anova" and the argument assurance is specified, the necessary sample size per group returned by the function with assurance specified is slightly underestimated. The method to obtain exact sample size in the above situation has not been developed yet. A practical solution is to use the sample size returned as the starting value to conduct a priori Montre Carlo simulations with function ss.aipe.sc.ancova.sensitivity, as discussed in Lai & Kelley (under review).

Author(s)

Keke Lai (University of California–Merced)

References

Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 1–24.

Kelley, K., & Rausch, J. R. (2006). Sample size planning for the standardized mean difference: Accuracy in Parameter Estimation via narrow confidence intervals. Psychological Methods, 11 (4), 363–385.

Lai, K., & Kelley, K. (2012). Accuracy in parameter estimation for ANCOVA and ANOVA contrasts: Sample size planning via narrow confidence intervals. British Journal of Mathematical and Statistical Psychology, 65, 350–370.

Steiger, J. H., & Fouladi, R. T. (1997). Noncentrality interval estimation and the evaluation of statistical methods. In L. L. Harlow, S. A. Mulaik, & J.H. Steiger (Eds.), What if there were no significance tests? (pp. 221–257). Mahwah, NJ: Lawrence Erlbaum.

See Also

ss.aipe.sc, ss.aipe.sc.ancova.sensitivity

Examples

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## Not run: 
ss.aipe.sc.ancova(psi=.8, width=.5, c.weights=c(.5, .5, 0, -1))

ss.aipe.sc.ancova(psi=.8, ratio=.6, width=.5, 
c.weights=c(.5, .5, 0, -1), divisor="s.anova")

ss.aipe.sc.ancova(psi=.5, rho=.4, width=.3, 
c.weights=c(.5, .5, 0, -1), divisor="s.anova")

## End(Not run)

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