# R/HyunhFeldtEpsilon.R In superb: Summary Plots with Adjusted Error Bars

#### Documented in HyunhFeldtEpsilon

```##############################################################
#' @title Hyunh and Feldt's epsilon measure of sphericity
#'
#' @description HyunhFeldtEpsilon() is a measure of sphericity created by
#' \insertCite{gg58;textual}{superb}. The original measure was biased
#' and therefore, \insertCite{hf76;textual}{superb} produced a revised version
#' (note that the 1976 paper contained typos that were uncorrected
#' in SPSS; \insertCite{l91;textual}{superb})
#'
#' @md
#'
#' @param dta a data.frame
#' @param cols a vector of column names indicating the relevant
#' columns on which to compute epsilon. Any other columns are ignored.
#'
#' @return returns the Hyunh-Feldt estimate of sphericity epsilon
#'
#' @references
#'  \insertAllCited{}
#'
#' @export HyunhFeldtEpsilon
#'

# from Chartier & Cousineau, TMJ, 2011
HyunhFeldtEpsilon <- function(dta, cols) {
# takes as input a data frame and column names of the measures
X     <- dta[cols]

# Get basic descriptive statistics
c     <- length(X)
n     <- dim(X)
S     <- cov(X)

# collapse the matrix
smjj  <- mean(diag(S))
sm    <- mean(colMeans(S))
sm2   <- sum(colMeans(S)^2)

num   <- c^2*(smjj-sm)^2
denom <- (c-1)*(sum(sum(S^2))-2*c*sm2+c^2*sm^2)
epsGG <- num / denom
epsGG

}
```

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superb documentation built on Jan. 23, 2023, 5:44 p.m.