var_mean: The variance of the weighted mean of assessments

View source: R/var_mean.R

var_meanR Documentation

The variance of the weighted mean of assessments

Description

This function calculates the variance of the weighted mean of a set of unit-standardized assessments. When the assessments are imperfectly correlated, this variance will be less than one. The identification cut score must be adjusted accordingly to maintain the desired percentile cutoff.

Usage

var_mean(r, w = NA)

Arguments

r

Either a correlation matrix or a vector of unique correlations. If the weights are not all equal, it is recommended to specify the correlations as a matrix to avoid erronous pairings of assessment correlations and weights, since this can be confusing if the correlations are supplied as a vector.

w

A vector of weights. Will be internally normalized to sum to 1 and presumes the same order of assessments as the correlation matrix. If omitted, it is assumed that all assessments have the same weight.

Details

The value returned by this function can be interpreted as the shrinkage factor of the variance of the weighted mean. The square root of this value is the shrinkage factor of the standard deviation of the weighted mean.

Examples

var_mean(r = c(.4, .7, .9), w = c(1, 2, 3))

var_mean(r = matrix(c(
  1, .4, .7,
  .4, 1, .9,
  .7, .9, 1
), 3, 3, byrow = TRUE))

mcbeem/giftedCalcs documentation built on May 3, 2022, 3:34 a.m.