metagear-expansion: metagearcomcon

#' @title Hedge's D for common control
#' 
#' @param table
#' @param X.t.a Column label for the means (X) of the treatment group (t) in group a
#' @param SD.t.a Column label for the standard deviations (SD) of the treatmet group in group a
#' @param N.t.a Column label for the sample sizes (N) of the treatment group in group a
#' @param X.c.a Column label for the means of the control group (c) in group a
#' @param SD.c.a Column label for the standard deviations of the control group in group a
#' @param N.c.a Column label for the sample sizes of the control group in group a
#' @param X.t.b Column label for the means of the treatment group in group b
#' @param SD.t.b Column label for the standard deviations of the treatment group in group b
#' @param N.t.b Column label for the sample sizes of the treatment group in group b
#' @param X.c.b Column label for the means of the control group in group b
#' @param SD.c.b Column label for the standard deviations of the control group in group b
#' @param N.c.b Column label for the sample sizes of the control group in group b
#' 
#' @return Hedge's D, variance, and covariance 
#' 
#' @description HedgesD calculates the Hedge's D, the variance, and the covariance for two data inputs that share the X, SD, and N of a control group and returns these values as a vector
#' 
#' @example #Note that "Dtest" is the name of an imported table
#' HedgesD(Dtest) 



HedgesD <- function (x) {
  D.df <- data.frame(
    SOURCE = c("X.t.a", "SD.t.a", "N.t.a", "X.c.a", "SD.c.a", "N.c.a", 
               "X.t.b", "SD.t.b", "N.t.b", "X.c.b", "SD.c.b", "N.c.b")
  )
  #X.t.a = mean of treatment in group a
  #SD.t.a = standard deviation of treatmet in group a
  #N.t.a = sample size of treatment in group a
  #X.c.a = mean of control in group a
  #SD.c.a = standard deviation of control in group a
  #N.c.a = sample size of control in group a
  #X.t.b = mean of treatment in group b
  #SD.t.b = standard deviation of treatmet in group b
  #N.t.b = sample size of treatment in group b
  #X.c.b = mean of control in group b
  #SD.c.b = standard deviation of control in group b
  #N.c.b = sample size of control in group b
  
  num.1a <- (N.c.a - 1) * (SD.c.a^2)
  num.2a <- (N.t.a - 1) * (SD.t.a^2)
  num.a <- num.1a + num.2a
  dem.a <- (N.c.a + N.t.a) - 2
  S.tot.a <- sqrt(num.a/dem.a)
  J.a <- 1 - (3 / (4 * (N.t.a + N.c.a) - 9))  
  d.1a <- (X.t.a - X.c.a)/S.tot.a 
  d.2a <- d.1a * J.a
  
  v.1a <- (1 / N.t.a) + (1 / N.c.a)
  v.2a <- d.2a^2 / (2 * (N.t.a + N.c.a))
  v.3a <- v.1a + v.2a
  
  num.1b <- (N.c.b - 1) * (SD.c.b^2)
  num.2b <- (N.t.b - 1) * (SD.t.b^2)
  num.b <- num.1b + num.2b
  dem.b <- (N.c.b + N.t.b) - 2
  S.tot.b <- sqrt(num.b/dem.b)
  J.b <- 1 - (3 / (4 * (N.t.b + N.c.b) - 9))  
  d.1b <- (X.t.b - X.c.b)/S.tot.b 
  d.2b <- d.1b * J.b
  
  v.1b <- (1 / N.t.b) + (1 / N.c.b)
  v.2b <- d.2b^2 / (2 * (N.t.b + N.c.b))
  v.3b <- v.1b + v.2b
  
  N.c <- N.c.a + N.c.b
  cov.d1 <- (d.2a * d.2b) / (2 * (N.c + N.t.a + N.t.b))
  cov.d <- cov.d1 + (1 / N.c)
  
  return(c(d.2a, v.3a, d.2b, v.3b, cov.d))
         
}