Can we really CONCLUDE that c is true??
Strictly speaking, random allocation will not ensure that the
baseline characteristics of both groups will be the same, merely that any
differences will be due to chance. By chance such differences will be
statistically significant for 1 in every 20 samplings on each measure or
conversely for 1 in every 20 measures on each sampling at the p = 0.005
level. By definition the frequency of such statistical difference will not
depend on the sample size. However, sample size and variance will effect
the respective standard mean errors/confidence intervals of each measure
in the sample as a whole and in each random allocation group. Random
allocation groups with wide confidence intervals relative to the value of
the mean of a measure should be treated with suspicion regardless of
whether or not the intervals overlap.
Competing interests: No competing interests