ss.aipe.c.ancova.sensitivity function

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

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

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

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.

Returns

  • 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; Lai.15@ND.Edu )

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)
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