psychmeta (version 1.0.2)

correct_r_uvdrr: Correct correlations for Case II direct range restriction and measurement error

Description

Correct correlations for Case II direct range restriction and measurement error

Usage

correct_r_uvdrr(rxyi, ux = 1, rxx = 1, ryy = 1, ux_observed = TRUE,
  rxx_restricted = TRUE, rxx_type = "alpha", ryy_restricted = TRUE,
  n = NULL, conf_level = 0.95, correct_bias = FALSE)

Arguments

rxyi

Vector of observed correlations.

ux

Vector of u ratios for X.

rxx

Vector of reliability coefficients for X.

ryy

Vector of reliability coefficients for Y.

ux_observed

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

rxx_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.

rxx_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.

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.

n

Optional vector of sample sizes associated with the rxyi correlations.

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).

Value

Data frame(s) of observed correlations (rxyi), operational range-restricted correlations corrected for measurement error in Y only (rxpi), operational range-restricted correlations corrected for measurement error in X only (rtyi), and range-restricted true-score correlations (rtpi), range-corrected observed-score correlations (rxya), operational range-corrected correlations corrected for measurement error in Y only (rxpa), operational range-corrected correlations corrected for measurement error in X only (rtya), and range-corrected true-score correlations (rtpa).

Details

$$\left[\frac{\rho_{XY_{i}}}{u_{X}\sqrt{\rho_{YY_{i}}}\sqrt{\left(\frac{1}{u_{X}^{2}}-1\right)\frac{\rho_{XY_{i}}^{2}}{\rho_{YY_{i}}}+1}}\right]/\sqrt{\rho_{XX_{a}}}$$else(rxyi / (ux * sqrt(ryyi) * sqrt((1 / ux^2 - 1) * rxyi^2 / ryyi + 1))) / sqrt(rxxa)

References

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<U+2013>612. https://doi.org/10.1037/0021-9010.91.3.594

Examples

# NOT RUN {
correct_r_uvdrr(rxyi = .3, ux = .8, rxx = .8, ryy = .8,
     ux_observed = TRUE, rxx_restricted = TRUE, ryy_restricted = TRUE)
correct_r_uvdrr(rxyi = .3, ux = .8, rxx = .8, ryy = .8,
     ux_observed = TRUE, rxx_restricted = TRUE, ryy_restricted = TRUE, n = 100)
# }