Calculating effect sizes between 3 groups for a set of variables in a dataset

Question

I would like to calculate the effect sizes of 3 treatments on 3 variables (x1, x2, x3). Suppose I have the following dataset:

set.seed(1234)

data <- data.frame(
  dose=factor(c(rep(1,25), rep(2,35), rep(3,40)), 
         labels = c("low", "middle", "high")),
  x1 = rnorm(100, 0, 2),
  x2 = rnorm(100, 3, 3),
  x3 = rnorm(100, 9, 4)
)

Now, I would like to calculate, for each combination of treatments, its effect size. I have found this function to calculate Cohen's d.

cohens_d <- function(x, y) {
  lx <- length(x)- 1
  ly <- length(y)- 1
  md  <- abs(mean(x) - mean(y))
  csd <- lx * var(x) + ly * var(y)
  csd <- csd/(lx + ly)
  csd <- sqrt(csd)

  cd  <- md/csd
  # Hedges'g 
  cd*(1-(3/(4*(length(x)+length(y)-9))))
  #print(cd)

}

Thank you very much for your help.

EDIT:

For example, below I can compute the effect size of the three treatments (pairwise) in one variable x1. Ideally, I would like a generalizable way to get these pairwise comparisons for all the variables in my dataset.

cohens_d(data$x1[data$dose=="low"], data$x1[data$dose=="middle"])
cohens_d(data$x1[data$dose=="low"], data$x1[data$dose=="high"])
cohens_d(data$x1[data$dose=="middle"], data$x1[data$dose=="high"])

Answer 1

df1$dose <- as.character(df1$dose)  # convert dose from factor to character
selected_cols <- colnames( df1 )[2:4]  # select columns prefixed with 'x'

library("reshape2")  # load reshape2 library
df1 <- melt( data = df1, id = "dose", measure.vars =selected_cols , value.name = 'value')  # melt df1 data frame

# compute cohensD    
cohens_df1 <- with(df1, sapply( selected_cols, # loop through column names
                                function( x ) combn( unique(dose), 2 ,  # loop through pairs of dose combinations
                                                     function( y ) cohens_d( df1[ variable %in% x & dose %in% y[1], 'value' ], 
                                                                             df1[ variable %in% x & dose %in% y[2], 'value' ] ))))

# assign row names 
rownames(cohens_df1) <- combn( unique(df1$dose), 2 , function( y ) paste( y, collapse = '_' ) )
cohens_df1
#                    x1         x2          x3
# low_middle  0.3319591 0.09511378 0.321519422
# low_high    0.4982017 0.03265765 0.337651450
# middle_high 0.8221889 0.10799662 0.006570862

Data:

set.seed(1234)    
df1 <- data.frame( dose = factor(c(rep(1,25), rep(2,35), rep(3,40)), levels = c(1, 2, 3), labels = c("low", "middle", "high")),
                   x1 = rnorm(100, 0, 2),
                   x2 = rnorm(100, 3, 3),
                   x3 = rnorm(100, 9, 4))