Some inference procedures for monotonically ordered normal means

This paper determines a limiting distribution of the estimated maximum and range of a set of monotonically ordered normal means when all means are in fact equal. The upper percentiles of the studentized distributions are tabulated. These percentiles can be used as critical values in tests of hypotheees concerning monotonically ordered normal means, and in forming simultaneons confidence limits for contrasts between normal means when the contrast coefficients are restricted to being monotonically ordered.