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

ss.aipe.sc.ancova.sensitivityR Documentation

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.