Abstract
In the one-way layout assuming that the underlying distribution is normal, we may execute Tukey-Kramer multiple comparisons procedure for searching all pairwise differences of locations. For the unequal sample sizes, the Tukey-Kramer (T-K) method is conservative. The T-K method is given by using the upper α point of the studentized range distribution A(t). A(t) is a lower bound for the distribution of the statistic max_<1≤i<i'≤k>|T_<ii'>|. We derive the distribution B(t) which gives an upper bound for the distribution of max_<1≤i<i'≤k>|T_<ii'>|. By using numerical double integration, we show that the value of B(t) is a little larger than that of A(t). As the result, we may verify that the conservativeness of the T-K method is small.
