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 a = 0.05, 0.01 and new tables for significance levels a = 0.10, 0.005, 0.001-all with sample sizes n = 2(1)20 (2)40(10)100 and degrees of freedom P = 1(1)20, 24, 30, 40, 60, 120, •.

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The following tables, together 'ith brief discussions cf methods of computation and uses, are included: (1) a nine-decirnal.place table of the incomplete Gamma-function ratio, I(up), for p=-0. 95(0.05)4 and u at intervals of 0. 1; and (2) a six-significant-figure table of the percentage points, corresponding to cumulative probabilities P= .0001, .0005, .001,. 005,. 01, .025•. 05, , 1(. 1) .9, .95, .975, 99, .995, 999, .9995 , and. 9999, of the chi-square distribution with vi 0. 1 (0. 1) 10 degrees of freedom. Both tables are accurate to within a unit in the last place.