t.2.sample <- function(m.1,m.2,s.1,s.2,n.1,
                       n.2,alpha=0.05,tails=2){
# compute sigma.hat.squared
  df <- n.1 + n.2 -2
  sigma.hat.squared <-( (n.1-1)*s.1^2 +(n.2-1)*s.2^2 )/df
# compute t
  t <- (m.1 - m.2) / sqrt((1/n.1 + 1/n.2)*sigma.hat.squared)
# compute critical value
  if(tails == -1) p <- alpha
  if(tails == 1) p <- 1-alpha
  if(tails == 2) p <- c(alpha/2,1 - alpha/2)
  crit <- qt(p,df)
# create a list of named quantities and return it
  res <- list(t.statistic = t, df = df, alpha = alpha, 
              critical.t.values = crit)
  return(res)
}

t.2.sample.ci <- function(m.1,m.2,s.1,s.2,n.1,
                       n.2,conf=.95){
# compute sigma.hat.squared
  df <- n.1 + n.2 -2
  sigma.hat.squared <-( (n.1-1)*s.1^2 +(n.2-1)*s.2^2 )/df
  se.diff <- sqrt((1/n.1 + 1/n.2)*sigma.hat.squared)
  alpha <- 1 - conf
  p <- 1 - alpha/2
  t.crit <- qt(p,df)
  diff <- t.crit * se.diff
  lower <- m.1-m.2 - diff
  upper <- m.1-m.2 + diff
  res <- list(lower.limit=lower,upper.limit=upper,confidence.level = conf)
  return(res)
}