ss.aipe.c.ancova.sensitivity {MBESS}R Documentation

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 conficence 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; Lai.15@ND.Edu)

Examples

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=10, 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=10, 
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)


[Package MBESS version 2.0.0 Index]