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

In MBESS: The MBESS R Package

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

Description

Sensitivity analysis for the sample size planning method with the goal to obtain sufficiently narrow confidence intervals for standardized ANCOVA complex contrasts.

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 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 detail 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 reasonable 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 confidence intervals
median.full.width	median width of the obtained full confidence 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

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.ancova; ss.aipe.sc.sensitivity

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