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Confidence Intervals for Correlations with Optional Design-Effect Adjustment

Source: R/estimateCIs.R
calculateCIs.Rd

Compute confidence intervals (CIs) for correlation coefficients using either Fisher's \(r \rightarrow z\) approach (Raykov-style on the \(z\) scale) or a Wald CI on the \(r\) scale. Standard errors are first **adjusted** by a design-effect factor when available, and optionally for double entry. The adjusted standard errors are used for all calculations, including CIs, z-tests, and p-values.

Usage

calculateCIs(
  tbl,
  rho_var,
  se_var,
  doubleentered = FALSE,
  method = "raykov",
  adjust_base = 1,
  design_effect_m = NULL,
  design_effect_rho = NULL,
  design_effect_m_col = NULL,
  design_effect_rho_col = NULL,
  conf_level = 0.95
)

Arguments

tbl

A data frame or tibble containing the correlation coefficient and standard error variables.

rho_var

The name of the column in tbl that contains the correlation coefficients.

se_var

The name of the column in tbl that contains the standard errors.

doubleentered

Logical. If TRUE, the function assumes that the correlation coefficients are double-entered, which adjusts the standard errors accordingly. Default is FALSE.

method

Character; CI method selector. Supported values:

  • "raykov" — Fisher \(r \rightarrow z\) CI (back-transformed).

  • "fisherz" — alias of "raykov".

  • "wald" — Wald CI on the \(r\) scale.

  • "doubleentered" — like "raykov" and, if doubleentered was not explicitly provided, it is set to TRUE (applies the \(\sqrt{2}\) multiplier).

  • "doubleenteredconserv" — like "wald" and, if doubleentered was not explicitly provided, it is set to TRUE.

adjust_base

A numeric value to adjust the standard errors. Default is 1.

design_effect_m

A numeric value for the design effect related to the mean. Default is NULL.

design_effect_rho

A numeric value for the design effect related to the correlation. Default is NULL.

design_effect_m_col

A character string specifying the column name for the design effect related to the mean. Default is NULL.

design_effect_rho_col

A character string specifying the column name for the design effect related to the correlation. Default is NULL.

conf_level

The confidence level for the intervals. Default is 0.95.

Value

A modified version of tbl with additional columns for the confidence intervals and related statistics. Everything uses adjusted standard errors, including confidence intervals, z-tests, and p-values.

Note

Double-entry handling and design effects are governed by doubleentered, design_effect_m/design_effect_rho (or their *_col variants), and adjust_base. The "doubleentered*" method values simply provide convenient aliases: they toggle doubleentered to TRUE only when the user hasn't explicitly set it, and map to "raykov" or "wald" as described.

Examples

tbl <- data.frame(rho = c(0.5, 0.7, 0.3), se = c(0.1, 0.2, 0.05))
calculateCIs(tbl, rho_var = "rho", se_var = "se", method = "raykov")
#>   rho   se     rho_z     se_sez se_se_adjusted se_sez_adjusted rho_plusse
#> 1 0.5 0.10 0.5493061 0.13333333           0.10      0.13333333  0.6699402
#> 2 0.7 0.20 0.8673005 0.39215686           0.20      0.39215686  0.9268992
#> 3 0.3 0.05 0.3095196 0.05494505           0.05      0.05494505  0.3945774
#>   rho_minusse rho_ztest  rho_zp1tail  rho_zp2tail rho_wald rho_waldp1tail
#> 1  0.28027235  4.119796 1.896039e-05 3.792079e-05      5.0   2.866516e-07
#> 2  0.09836807  2.211616 1.349659e-02 2.699319e-02      3.5   2.326291e-04
#> 3  0.19913270  5.633257 8.841892e-09 1.768378e-08      6.0   9.865876e-10
#>   rho_waldp2tail
#> 1   5.733031e-07
#> 2   4.652582e-04
#> 3   1.973175e-09