ss.aipe.c.ancova.sensitivity: Sensitivity analysis for sample size planning for the...

In MBESS: The MBESS R Package

Sensitivity analysis for sample size planning for the (unstandardized) contrast in randomized ANCOVA from the Accuracy in Parameter Estimation (AIPE) Perspective

Description

Performs a sensitivity analysis when planning sample size from the Accuracy in Parameter Estimation (AIPE) Perspective for the (unstandardized) contrast in randomized ANCOVA design.

Usage

ss.aipe.c.ancova.sensitivity(true.error.var.ancova = NULL, 
est.error.var.ancova = NULL, true.error.var.anova = NULL, 
est.error.var.anova = NULL, rho, est.rho = NULL, G = 10000, 
mu.y, sigma.y, mu.x, sigma.x, c.weights, width,
conf.level = 0.95, assurance = NULL, certainty=NULL)

Arguments

true.error.var.ancova	population error variance of the ANCOVA model
est.error.var.ancova	estimated error variance of the ANCOVA model
true.error.var.anova	population error variance of the ANOVA model (i.e., excluding the covariate)
est.error.var.anova	estimated error variance of the ANOVA model (i.e., excluding the covariate)
rho	population correlation coefficient of the response and the covariate
est.rho	estimated correlation coefficient of the response and the covariate
G	number of generations (i.e., replications) of the simulation
mu.y	vector that contains the response's population mean of each group
sigma.y	the population standard deviation of the response
mu.x	the population mean of the covariate
sigma.x	the population standard deviation of 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

The arguments mu.y, mu.x, sigma.y, and sigma.x are used to generate random data in the simulations for the sensitivity analysis. The value of mu.y should be the same as the square root of true.error.var.anova

So far this function is based on one-covariate randomized ANCOVA design only. The argument mu.x should be a single number, because it is assumed that the population mean of the covariate is equal across groups in randomized ANCOVA.

Value

Psi.obs	the observed (unstandardized) contrast
se.Psi	the standard error of the observed (unstandardized) contrast
se.Psi.restricted	the standard error of the observed (unstandardized) contrast calculated by ignoring the covariate
se.res.over.se.full	the ratio of contrast's full standard error over the restricted one in each iteration
width.obs	full confidence interval width
Type.I.Error	Type I error happens in each iteration
Type.I.Error.Upper	Type I error happens in the upper end in each iteration
Type.I.Error.Lower	Type I error happens in the lower end in each iteration
Type.I.Error	percentage of Type I error happened in the entire simulation
Type.I.Error.Upper	percentage of Type I error happened in the upper end in the entire simulation
Type.I.Error.Lower	percentage of Type I error happened in the lower end in the entire simulation
width.NARROWER.than.desired	percentage of obtained widths that are narrower than the desired width
Mean.width.obs	mean width of the obtained full confidence intervals
Median.width.obs	median width of the obtained full confidence intervals
Mean.se.res.vs.se.full	the mean of the ratios of contrast's full standard error over the restricted one
Psi.pop	population (unstandardized) contrast
Contrast.Weights	contrast weights
mu.y	the response's population mean of each group
mu.x	the population mean of the covariate
sigma.x	the population standard deviation of the covariate
Sample.Size.per.Group	sample size per group
conf.level	the desired confidence interval coverage, (i.e., 1 - Type I error rate)
assurance	specified assurance
rho	population correlation coefficient of the response and the covariate
est.rho	estimated correlation coefficient of the response and the covariate
true.error.var.ANOVA	population error variance of the ANOVA model
est.error.var.ANOVA	estimated error variance of the ANOVA model

Author(s)

Keke Lai (University of Notre Dame; [e-mail])

Examples

## Not run: 
ss.aipe.c.ancova.sensitivity(true.error.var.ancova=30, 
est.error.var.ancova=30, rho=.2, mu.y=c(10,12,15,13), mu.x=2, 
G=1000, sigma.x=1.3, sigma.y=2, c.weights=c(1,0,-1,0), width=3)

ss.aipe.c.ancova.sensitivity(true.error.var.anova=36, 
est.error.var.anova=36, rho=.2, est.rho=.2, G=1000, 
mu.y=c(10,12,15,13), mu.x=2, sigma.x=1.3, sigma.y=6, 
c.weights=c(1,0,-1,0), width=3, assurance=NULL)

## End(Not run)

MBESS documentation built on Oct. 26, 2023, 9:07 a.m.