brokentrans: Artificial dataset that suffers with broken transitivity of...
In paircompviz: Multiple comparison test visualization

This is a dataset of artificial data created to demonstrate that there exists a data sample such that pairwise comparisons using t-test break transitivity of the results, i.e. that if treatment 1 is significantly lower than 2 and treatment 2 is lower than 3, it is not always the case that also treatment 1 is significantly lower than 3.

1	data(brokentrans)

A data frame of two columns:

x is the measured value,
g is the treatment group.

  data(brokentrans)

  # For \alpha = 10^{-9}, we obtain significant difference
  # between 1-2, 2-3, but not 1-3.
  tapply(brokentrans$x, brokentrans$g, mean)
  pairwise.t.test(brokentrans$x, brokentrans$g, pool.sd=FALSE)