DMAR (version 1.0.0)

ss_aipe_src: Sample Size Necessary for the Accuracy in Parameter Estimation Approach for a Standardized Regression Coefficient of Interest

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

ss_aipe_src(
  rho2_Y_X = NULL,
  Rho2_j_X_without_j = NULL,
  p = NULL,
  beta_j = NULL,
  width,
  which_width = "Full",
  sigma_Y = 1,
  sigma_X_j = 1,
  rho_XX = NULL,
  rho_YX = NULL,
  which_predictor = NULL,
  alpha_lower = NULL,
  alpha_upper = NULL,
  conf_level = 0.95,
  assurance = NULL
)

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.

Arguments

rho2_Y_X

Population value of the squared multiple correlation coefficient

Rho2_j_X_without_j

Population value of the squared multiple correlation coefficient predicting the jth predictor variable from the remaining p-1 predictor variables

p

The number of predictor variables

beta_j

The regression coefficient for the jth 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_j

The population standard deviation of the jth 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)

assurance

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

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.

Author

Ken Kelley [email protected]

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.

References

Kelley, K., & Maxwell, S. E. (2003). Sample size for multiple regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8(3), 305--321. tools:::Rd_expr_doi("10.1037/1082-989X.8.3.305")

Kelley, K., & Maxwell, S. E. (2008). Sample size planning with applications to multiple regression: Power and accuracy for omnibus and targeted effects. In P. Alasuutari, L. Bickman, & J. Brannen (Eds.), The Sage handbook of social research methods (pp. 166--192). Sage.

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapter 4 on individual comparisons of means and Chapter 6 on trend analysis.)

See Also

ss_aipe_reg_coef_sensitivity, ci_nc_t, ss_aipe_reg_coef, ss_aipe_rc

design_consequences for what a chosen design delivers: power, the Type S (sign) and Type M (exaggeration) errors of the significance filter, and the expected confidence interval width.

Examples

# 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_j = 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_j = 1, rho_XX = rho_XX,
            rho_YX = rho_YX, which_predictor = 1, conf_level = 1 - .05,
            assurance = .85)