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

Sensitivity analysis for the sample size planning method for standardized ANCOVA contrast

Description

Sensitivity analysis for the sample size planning method from the AIPE perspective for a standardized ANCOVA complex contrast.

Usage

ss.aipe.sc.ancova.sensitivity(true.psi = NULL, estimated.psi = NULL, 
c.weights, desired.width = NULL, selected.n = NULL, mu.x = 0, 
sigma.x = 1, rho, divisor = "s.ancova", assurance = NULL, 
conf.level = 0.95, G = 10000, print.iter = TRUE, detail = TRUE, ...)

Arguments

true.psi the population standardized ANCOVA contrast
estimated.psi the estimated standardized ANCOVA contrast
c.weights the contrast weights
desired.width the desired full width of the obtained confidence interval
selected.n selected sample size to use in order to determine distributional properties of at a given value of sample size
mu.x the population mean for the covariate
sigma.x the population standard deviation of the covariate
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"
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)
conf.level the desired confidence interval coverage, (i.e., 1 - Type I error rate)
G number of generations (i.e., replications) of the simulation
print.iter to print the current value of the iterations
detail whether the user needs a detailed (TRUE) or brief (FALSE) report of the simulation results; the detailde report includes all the raw data in the simulations
... 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.

The population mean and standard deviation of the covariate does not affect the sample size planning procedure; they can be specified as any values that are considered as reasonalbe by the user.

Value

psi.obs observed standardized contrast in each iteration
Full.Width vector of the full confidence interval width
Width.from.psi.obs.Lower vector of the lower confidence interval width
Width.from.psi.obs.Upper vector of the upper confidence interval width
Type.I.Error.Upper iterations where a Type I error occurred on the upper end of the confidence interval
Type.I.Error.Lower iterations where a Type I error occurred on the lower end of the confidence interval
Type.I.Error iterations where a Type I error happens
Lower.Limit the lower limit of the obtained confidence interval
Upper.Limit the upper limit of the obtained confidence interval
replications number of replications of the simulation
True.psi population standardized contrast
Estimated.psi estimated standardized contrast
Desired.Width the desired full width of the obtained confidence interval
assurance the value assigned to the argument assurance
Sample.Size.per.Group sample size per group
Number.of.Groups number of groups
mean.full.width mean width of the obtained full conficence intervals
median.full.width median width of the obtained full conficence intervals
sd.full.width standard deviation of the widths of the obtained full confidence intervals
Pct.Width.obs.NARROWER.than.desired percentage of the obtained full confidence interval widths that are narrower than the desired width
mean.Width.from.psi.obs.Lower mean lower width of the obtained confidence intervals
mean.Width.from.psi.obs.Upper mean upper width of the obtained confidence intervals
Type.I.Error.Upper Type I error rate from the upper side
Type.I.Error.Lower Type I error rate from the lower side
Type.I.Error Type I error rate

Author(s)

Keke Lai (University of Notre Dame, Lai.15@ND.Edu)

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. (2007). Sample size planning for standardized ANCOVA and ANOVA contrasts: Obtaining narrow confidence intervals. Manuscript submitted for publication.

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 where no significance tests? (pp. 221-257). Mahwah, NJ: Lawrence Erlbaum.


[Package MBESS version 2.0.0 Index]