# ss.aipe.src: sample size necessary for the accuracy in parameter... In MBESS: The MBESS R Package

## Description

A function used to plan sample size from the accuracy in parameter estimation approach for a standardized regression coefficient of interest given the input specification.

## Usage

 ```1 2 3 4 5 6``` ```ss.aipe.src(Rho2.Y_X = NULL, Rho2.k_X.without.k = NULL, K = NULL, beta.k = NULL, width, which.width = "Full", sigma.Y = 1, sigma.X.k = 1, RHO.XX = NULL, Rho.YX = NULL, which.predictor = NULL, alpha.lower = NULL, alpha.upper = NULL, conf.level = .95, degree.of.certainty = NULL, assurance=NULL, certainty=NULL, Suppress.Statement = FALSE) ```

## Arguments

 `Rho2.Y_X` Population value of the squared multiple correlation coefficient `Rho2.k_X.without.k` Population value of the squared multiple correlation coefficient predicting the kth predictor variable from the remaining p-1 predictor variables `K` the number of predictor variables `beta.k` the regression coefficient for the kth predictor variable (i.e., the predictor of interest) `width` the desired width of the confidence interval `which.width` which width (`"Full"`, `"Lower"`, or `"Upper"`) the width refers to (at present, only `"Full"` can be specified) `sigma.Y` the population standard deviation of Y (i.e., the dependent variables) `sigma.X.k` the population standard deviation of the kth X variable (i.e., the predictor variable of interest) `RHO.XX` Population correlation matrix for the p predictor variables `Rho.YX` Population p length vector of correlation between the dependent variable (Y) and the p independent variables `which.predictor` identifies which of the p predictors is of interest `alpha.lower` Type I error rate for the lower confidence interval limit `alpha.upper` Type I error rate for the upper confidence interval limit `conf.level` desired level of confidence for the computed interval (i.e., 1 - the Type I error rate) `degree.of.certainty` degree of certainty that the obtained confidence interval will be sufficiently narrow, which yields an approximate sample size to be verified with function `ss.aipe.reg.coef.sensitivity` to determine if it is appropriate. `assurance` an alias for `degree.of.certainty` `certainty` an alias for `degree.of.certainty` `Suppress.Statement` `TRUE/FALSE` statement whether or not a sentence describing the situation defined is printed with the necessary sample size

## Details

Not all of the arguments need to be specified, only those that provide all of the necessary information so that the sample size can be determined for the conditions specified.

## Value

Returns the necessary sample size in order for the goals of accuracy in parameter estimation to be satisfied for the confidence interval for a particular regression coefficient given the input specifications.

## Warning

As discussed in Kelley and Maxwell (2008), the sample size planning approach from the AIPE perspective used in this function is only an approximation.

## Note

This function calls upon `ss.aipe.reg.coef` in MBESS but has a different naming scheme. See `ss.aipe.reg.coef` for more details.

## Author(s)

Ken Kelley (University of Notre Dame; [email protected])

## References

Kelley, K. & Maxwell, S. E. (2003). Sample size for Multiple Regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8, 305–321.

Kelley, K. & Maxwell, S. E. (2008). Sample Size Planning with applications to multiple regression: Power and accuracy for omnibus and targeted effects. In P. Alasuuta, J. Brannen, & L. Bickman (Eds.), The Sage handbook of social research methods (pp. 166–192). Newbury Park, CA: Sage.

`ss.aipe.reg.coef.sensitivity`, `conf.limits.nct`, `ss.aipe.reg.coef`, `ss.aipe.rc`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```# Exchangable correlation structure # Rho.YX <- c(.3, .3, .3, .3, .3) # RHO.XX <- rbind(c(1, .5, .5, .5, .5), c(.5, 1, .5, .5, .5), c(.5, .5, 1, .5, .5), # c(.5, .5, .5, 1, .5), c(.5, .5, .5, .5, 1)) # ss.aipe.src(width=.1, which.width="Full", sigma.Y=1, sigma.X=1, RHO.XX=RHO.XX, # Rho.YX=Rho.YX, which.predictor=1, conf.level=1-.05) # ss.aipe.src(width=.1, which.width="Full", sigma.Y=1, sigma.X=1, RHO.XX=RHO.XX, # Rho.YX=Rho.YX, which.predictor=1, conf.level=1-.05, degree.of.certainty=.85) ```