psychmeta (version 2.7.0)

correct_d: Correct \(d\) values for measurement error and/or range restriction

Description

This function is a wrapper for the correct_r() function to correct \(d\) values for statistical and psychometric artifacts.

Usage

correct_d(
  correction = c("meas", "uvdrr_g", "uvdrr_y", "uvirr_g", "uvirr_y", "bvdrr", "bvirr"),
  d,
  ryy = 1,
  uy = 1,
  rGg = 1,
  pi = NULL,
  pa = NULL,
  uy_observed = TRUE,
  ryy_restricted = TRUE,
  ryy_type = "alpha",
  k_items_y = NA,
  sign_rgz = 1,
  sign_ryz = 1,
  n1 = NULL,
  n2 = NA,
  conf_level = 0.95,
  correct_bias = FALSE
)

Value

Data frame(s) of observed \(d\) values (dgyi), range-restricted \(d\) values corrected for measurement error in Y only (dgpi), range-restricted \(d\) values corrected for measurement error in the grouping variable only (dGyi), and range-restricted true-score \(d\) values (dGpi), range-corrected observed-score \(d\) values (dgya), range-corrected \(d\) values corrected for measurement error in Y only (dgpa), range-corrected \(d\) values corrected for measurement error in the grouping variable only (dGya), and range-corrected true-score \(d\) values (dGpa).

Arguments

correction

Type of correction to be applied. Options are "meas", "uvdrr_g", "uvdrr_y", "uvirr_g", "uvirr_y", "bvdrr", "bvirr"

d

Vector of \(d\) values.

ryy

Vector of reliability coefficients for Y (the continuous variable).

uy

Vector of u ratios for Y (the continuous variable).

rGg

Vector of reliabilities for the group variable (i.e., the correlations between observed group membership and latent group membership).

pi

Proportion of cases in one of the groups in the observed data (not necessary if n1 and n2 reflect this proportionality).

pa

Proportion of cases in one of the groups in the population.

uy_observed

Logical vector in which each entry specifies whether the corresponding uy value is an observed-score u ratio (TRUE) or a true-score u ratio. All entries are TRUE by default.

ryy_restricted

Logical vector in which each entry specifies whether the corresponding rxx value is an incumbent reliability (TRUE) or an applicant reliability. All entries are TRUE by default.

ryy_type

String vector identifying the types of reliability estimates supplied (e.g., "alpha", "retest", "interrater_r", "splithalf"). See the documentation for ma_r() for a full list of acceptable reliability types.

k_items_y

Numeric vector identifying the number of items in each scale.

sign_rgz

Vector of signs of the relationships between grouping variables and the selection mechanism.

sign_ryz

Vector of signs of the relationships between Y variables and the selection mechanism.

n1

Optional vector of sample sizes associated with group 1 (or the total sample size, if n2 is NULL).

n2

Optional vector of sample sizes associated with group 2.

conf_level

Confidence level to define the width of the confidence interval (default = .95).

correct_bias

Logical argument that determines whether to correct error-variance estimates for small-sample bias in correlations (TRUE) or not (FALSE). For sporadic corrections (e.g., in mixed artifact-distribution meta-analyses), this should be set to FALSE (the default).

References

Alexander, R. A., Carson, K. P., Alliger, G. M., & Carr, L. (1987). Correcting doubly truncated correlations: An improved approximation for correcting the bivariate normal correlation when truncation has occurred on both variables. Educational and Psychological Measurement, 47(2), 309–315. tools:::Rd_expr_doi("10.1177/0013164487472002")

Dahlke, J. A., & Wiernik, B. M. (2020). Not restricted to selection research: Accounting for indirect range restriction in organizational research. Organizational Research Methods, 23(4), 717–749. tools:::Rd_expr_doi("10.1177/1094428119859398")

Hunter, J. E., Schmidt, F. L., & Le, H. (2006). Implications of direct and indirect range restriction for meta-analysis methods and findings. Journal of Applied Psychology, 91(3), 594–612. tools:::Rd_expr_doi("10.1037/0021-9010.91.3.594")

Le, H., Oh, I.-S., Schmidt, F. L., & Wooldridge, C. D. (2016). Correction for range restriction in meta-analysis revisited: Improvements and implications for organizational research. Personnel Psychology, 69(4), 975–1008. tools:::Rd_expr_doi("10.1111/peps.12122")

Schmidt, F. L., & Hunter, J. E. (2015). Methods of meta-analysis: Correcting error and bias in research findings (3rd ed.). Sage. tools:::Rd_expr_doi("10.4135/9781483398105"). pp. 43–44, 140–141.

Examples

## Correction for measurement error only
correct_d(correction = "meas", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = .7, pa = .5)
correct_d(correction = "meas", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = NULL, pa = .5, n1 = 100, n2 = 200)

## Correction for direct range restriction in the continuous variable
correct_d(correction = "uvdrr_y", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = .7, pa = .5)
correct_d(correction = "uvdrr_y", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = NULL, pa = .5, n1 = 100, n2 = 200)

## Correction for direct range restriction in the grouping variable
correct_d(correction = "uvdrr_g", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = .7, pa = .5)
correct_d(correction = "uvdrr_g", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = NULL, pa = .5, n1 = 100, n2 = 200)

## Correction for indirect range restriction in the continuous variable
correct_d(correction = "uvdrr_y", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = .7, pa = .5)
correct_d(correction = "uvdrr_y", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = NULL, pa = .5, n1 = 100, n2 = 200)

## Correction for indirect range restriction in the grouping variable
correct_d(correction = "uvirr_g", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = .7, pa = .5)
correct_d(correction = "uvirr_g", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = NULL, pa = .5, n1 = 100, n2 = 200)

## Correction for indirect range restriction in the continuous variable
correct_d(correction = "uvdrr_y", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = .7, pa = .5)
correct_d(correction = "uvdrr_y", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = NULL, pa = .5, n1 = 100, n2 = 200)

## Correction for direct range restriction in both variables
correct_d(correction = "bvdrr", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = .7, pa = .5)
correct_d(correction = "bvdrr", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = NULL, pa = .5, n1 = 100, n2 = 200)

## Correction for indirect range restriction in both variables
correct_d(correction = "bvirr", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = .7, pa = .5)
correct_d(correction = "bvirr", d = .5, ryy = .8, uy = .7,
          rGg = .9, pi = NULL, pa = .5, n1 = 100, n2 = 200)