David B. Duncan [2] has formulated a new multiple range test making use of special protection levels based upon degrees of freedom. Duncan [Tables II and III] has also tabulated the critical values (significant studentized ranges) for 5 percent and 1 percent level new multiple range tests, based upon tables by Pearson and Hartley [8] and by Beyer [1]. Unfortunately, there are sizable errors in some of the published critical values. This fact was discovered and reported by the author [4], who instigated the computation at Wright-Patterson Air Force Base of more accurate tables of the probability integrals of the range and of the studentized range than those published by Pearson and Hartley [7, 8]. This extensive computing project, of which one of the primary objectives was the determination of more accurate critical values for Duncan's test, has now been completed. The purpose of this paper is to report critical values (to four significant figures) which have been found by inverse interpolation in the new table of the probability integral of the studentized range. Included are corrected tables for significance levels α = 0.05, 0.01 and new tables for significance levels α = 0.10, 0.005, 0.001-all with sample sizes n = 2(1)20(2)40(10)100 and degrees of freedom ν = 1(1)20, 24, 30, 40, 60, 120, ∞.