R/convert.R

Defines functions convert.means.to.d convert.ncf.to.omegasq convert.fisherz.to.r convert.b.to.t convert.omegasq.to.cohensf convert.omegasq.to.cohensfsq convert.omegasq.to.f convert.cohensfsq.to.omegasq convert.cohensf.to.omegasq convert.etasq.to.cohensf convert.f.to.omegasq convert.f.to.etasq convert.f.to.d convert.f.to.p convert.chisq.to.p convert.chisq.to.V convert.percentage.to.se convert.or.to.r convert.or.to.d convert.logodds.to.r convert.logodds.to.d convert.d.to.variance convert.d.to.logodds convert.d.to.t convert.d.to.r convert.t.to.d convert.t.to.p convert.t.to.r convert.r.to.fisherz convert.r.to.p convert.r.to.d convert.r.to.t

Documented in convert.b.to.t convert.chisq.to.p convert.chisq.to.V convert.cohensfsq.to.omegasq convert.cohensf.to.omegasq convert.d.to.logodds convert.d.to.r convert.d.to.t convert.d.to.variance convert.etasq.to.cohensf convert.fisherz.to.r convert.f.to.d convert.f.to.etasq convert.f.to.omegasq convert.f.to.p convert.logodds.to.d convert.logodds.to.r convert.means.to.d convert.ncf.to.omegasq convert.omegasq.to.cohensf convert.omegasq.to.cohensfsq convert.omegasq.to.f convert.or.to.d convert.or.to.r convert.percentage.to.se convert.r.to.d convert.r.to.fisherz convert.r.to.p convert.r.to.t convert.t.to.d convert.t.to.p convert.t.to.r

### See http://statistiki.eu/wiki/Converting_Effect_Sizes for some formulae

###########################################################################
### Converting from: Pearson's r
###########################################################################

convert.r.to.t <- function(r, n) {
  return(r * sqrt((n - 2) / (1-r^2)));
}

convert.r.to.d <- function(r) {
  return( (r*2) / sqrt(1 - r^2));
}

convert.r.to.p <- function(r, n) {
  t <- convert.r.to.t(r, n);
  return(convert.t.to.p(t, n - 2));
}

convert.r.to.fisherz <- function(r) {
  return(.5 * log((1+r) / (1-r)));
}

###########################################################################
### Converting from: Student's t
###########################################################################

convert.t.to.r <- function(t, n) {
  return(t / (sqrt(n-2+t^2)));
}

convert.t.to.p <- function(t, df) {
  return(2*pt(-abs(t),df));
}

convert.t.to.d <- function(t, df=NULL, n1=NULL, n2=NULL, proportion=.5) {
 
  if (is.null(df) && !is.null(n1) && !is.null(n2)) {
    groupSize1 <- n1;
    groupSize2 <- n2;
  }
  else if (!is.null(df) && is.null(n1) && is.null(n2)) {
    groupSize1 <-      proportion  * (df + 2);
    groupSize2 <- (1 - proportion) * (df + 2);
  }
  else {
    warning("Specify either df (and ideally proportion) or n1 and n2! Returning NA.");
    return(NA);
  }
  
  ### Updated to reflect http://journal.frontiersin.org/article/10.3389/fpsyg.2013.00863/full
#   multiplier <- sqrt(((groupSize1 + groupSize2) / (groupSize1 * groupSize2)) *
#                        ((groupSize1 + groupSize2) / (groupSize1 + groupSize2 - 2)));
  multiplier <- sqrt((1 / groupSize1) + (1 / groupSize2));
  
  d <- t * multiplier;
  
  return(d);
}

###########################################################################
### Converting from: Cohen's d
###########################################################################

convert.d.to.r <- function(d, n1 = NULL, n2 = NULL, akfEq8='if (n1 + n2) < 50') {
  if (!is.logical(akfEq8) && !is.null(n1) && !is.null(n2) && ((n1 + n2) < 50)) {
    akfEq8 <- TRUE;
  }
  if (is.logical(akfEq8) && akfEq8) {
    if (is.null(n1) || is.null(n2)) stop("Cannot use the equation by Aaron, Kromrey & Ferron (1998) is you do not specify both sample sizes!");
    N <- n2 + n2;
    return(sqrt( d^2 / ( d^2 + ((N^2 - 2 * N) / (n1 * n2)) ) ));
  } else {
    if (is.null(n1) || is.null(n2)) {
      a <- 4;
    } else {
      a <- (n1 + n2) ^ 2 / (n1 * n2)
    }
    return(d / sqrt(d^2 + a));
  }
}

convert.d.to.t <- function(d, df=NULL, n1=NULL, n2=NULL, proportion=.5) {
  ### Obsolete; not basing computation on
  ### reversal of formula used in e.g.
  ### http://journal.frontiersin.org/article/10.3389/fpsyg.2013.00863/full
  #   return(ifelse(d < 0,
  #                 -1 * sqrt(sqrt(n) * abs(d)),
  #                 sqrt(sqrt(n) * abs(d))));
  
  if (is.null(df) && !is.null(n1) && !is.null(n2)) {
    groupSize1 <- n1;
    groupSize2 <- n2;
  }
  else if (!is.null(df) && is.null(n1) && is.null(n2)) {
    groupSize1 <-      proportion  * (df + 2);
    groupSize2 <- (1 - proportion) * (df + 2);
  }
  else {
    warning("Specify either df (and ideally proportion) or n1 and n2! Returning NA.");
    return(NA);
  }
  
  multiplier <- sqrt((1 / groupSize1) + (1 / groupSize2));
  
  t <- d / multiplier;
  
  return(t);
  
}

convert.d.to.logodds <- function(d) {
  if (!is.numeric(d) || (length(d) > 1)) {
    stop("The 'd' argument is not a single numeric value!");
  }
  return(d * (pi / sqrt(3)));
}

convert.d.to.variance <- function(d, n1, n2) {
  return( (((n1+n2) / (n1*n2)) + ((d^2) / (2*(n1+n2-2)))) * ((n1+n2) / (n1+n2-2)) );
}

###########################################################################
### Converting from: Log Odds
###########################################################################

convert.logodds.to.d <- function(logodds) {
  return(logodds * (sqrt(3) / pi));
}

convert.logodds.to.r <- function(logodds) {
  return(convert.d.to.r(convert.logodds.to.d(logodds)));
}

###########################################################################
### Converting from: Odds Ratio
###########################################################################

convert.or.to.d <- function(or) {
  return(log(or) * (sqrt(3) / pi));
}

convert.or.to.r <- function(or) {
  return(convert.d.to.r(convert.logodds.to.d(log(or))));
}

###########################################################################
### Converting from: Proportions (percentages)
###########################################################################

convert.percentage.to.se <- function(p, n) {
  return(sqrt((p * (1-p)) / n));
}

###########################################################################
### Converting from: Chi Square
###########################################################################

convert.chisq.to.V <- function(chisq, n, minDim) {
  if (!is.numeric(chisq) || (length(chisq) > 1)) {
    stop("The 'chisq' argument is not a single numeric value!");
  }
  if (!is.numeric(n) || (length(n) > 1)) {
    stop("The 'n' argument is not a single numeric value!");
  }
  if (!is.numeric(minDim) || (length(minDim) > 1)) {
    stop("The 'minDim' argument is not a single numeric value!");
  }
  res <- as.numeric(sqrt(chisq/(n*(minDim - 1))));
  return(ifelse(is.finite(res), res, NA));
}

convert.chisq.to.p <- function(chisq, df, lower.tail=FALSE) {
  return(2*pchisq(chisq, df, lower.tail=lower.tail));
}

###########################################################################
### Converting from: F
###########################################################################

convert.f.to.p <- function(f, df1, df2, lower.tail=FALSE) {
  return(2*pf(f, df1, df2, lower.tail=lower.tail));
}

convert.f.to.d <- function(f, df1, df2 = NULL, n1=NULL, n2=NULL, proportion=.5) {
  if (df1 != 1) {
    warning("You can only convert an F value for the comparison of two groups to Cohen's d, ",
            "and you specified a df1 of ", df1, ", which means this F value concerns the comparison ",
            "of ", df1 + 1, " groups. Returning NA.");
    return(NA);
  }
  else if (is.null(df2) && !is.null(n1) && !is.null(n2)) {
    groupSize1 <- n1;
    groupSize2 <- n2;
  }
  else if (!is.null(df2) && is.null(n1) && is.null(n2)) {
    groupSize1 <- proportion * (df1 + df2 + 1);
    groupSize2 <- (1 - proportion) * (df1 + df2 + 1);
  }
  else {
    warning("Specify either df2 (and ideally proportion) or n1 and n2! Returning NA.");
    return(NA);
  }
  
  d <- sqrt(f * ((groupSize1 + groupSize2) / (groupSize1 * groupSize2)) *
              ((groupSize1 + groupSize2) / (groupSize1 + groupSize2 - 2)));
  
  return(d);
}

convert.f.to.etasq <- function(f, df1, df2) {
  return( (f * df1) / ((f * df1) + df2) );
}

convert.f.to.omegasq <- function(f, df1, df2) {
  return( (f - 1) / (f + (df2 + 1) / (df1)) );
}

###########################################################################
### Converting from: Eta square
###########################################################################

convert.etasq.to.cohensf <- function(etasq) {
  return(sqrt(etasq / (1-etasq)));
}

###########################################################################
### Converting from: Cohen's f^2
###########################################################################

### Equation 16 in Steiger's (2004) 'Beyond the F Test' paper

convert.cohensf.to.omegasq <- function(cohensf) {
  return(cohensf^2 / (1 + cohensf^2));
}

convert.cohensfsq.to.omegasq <- function(cohensfsq) {
  return(cohensfsq / (1 + cohensfsq));
}

###########################################################################
### Converting from: Omega^2
###########################################################################

convert.omegasq.to.f <- function(omegasq, df1, df2) {
  return( (omegasq * ((df2 + 1) / df1) + 1) / (1 - omegasq) );
}

### Equation 15 in Steiger's (2004) 'Beyond the F Test' paper

convert.omegasq.to.cohensfsq <- function(omegasq) {
  return(omegasq / (1 - omegasq));
}

convert.omegasq.to.cohensf <- function(omegasq) {
  return(sqrt(omegasq / (1 - omegasq)));
}

###########################################################################
### Converting from: Beta (regression weight)
###########################################################################

convert.b.to.t <- function(b, se) {
  return(b/se);
}

###########################################################################
### Converting from: Fisher's z
###########################################################################

convert.fisherz.to.r <- function(z) {
  return((exp(2 * z) - 1) / (exp(2*z)+1));
}

#########################################################################
### Converting from: Noncentrality parameter of the F distribution
#########################################################################

### Using formula 16 in Beyond The F Test, Steiger's 2004 paper

convert.ncf.to.omegasq <- function(ncf, N) {
  return(ncf / (ncf + N));
}

###########################################################################
### Converting from: Means and standard deviations
###########################################################################

convert.means.to.d <- function(means, sds, ns = NULL, var.equal=NULL) {
  if (is.null(ns)) {
    var <- mean(sds);
  } else {
    if (is.null(var.equal)) {
      ### Try to establish equality ourselves
      if (max(sds) < (3 * min(sds))) {
        ### Consider then equal
        var.equal <- TRUE;
      } else {
        ### Consider them different
        var.equal <- FALSE;
      }
    }
    if (var.equal) {
      ss1 <- sds[1]^2 * (ns[1] - 1);
      ss2 <- sds[2]^2 * (ns[2] - 1);
      var <- (ss1 + ss2) / (ns[1] + ns[2] - 2);
    } else {
      ### Take variance of smallest group
      var <- sds[ns == min(ns)] ^ 2;
    }
  }
  ### Compute difference between means and divide
  ### by standard deviation
  return((means[2] - means[1]) / sqrt(var));
}

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userfriendlyscience documentation built on May 2, 2018, 5:06 p.m.