MTB > read 'a:\ed257\mlapair.dat' c1 c2 20 ROWS READ ROW C1 C2 1 32 34 2 31 31 3 29 35 4 10 16 . . . MTB > describe c1-c2 N MEAN MEDIAN TRMEAN STDEV SEMEAN C1 20 25.80 27.00 26.28 6.30 1.41 C2 20 28.30 27.50 28.61 5.95 1.33 MIN MAX Q1 Q3 C1 10.00 33.00 22.25 31.00 C2 15.00 36.00 26.00 33.75 MTB > let c3 = c2 - c1 MTB > sinterval 95 c3 SIGN CONFIDENCE INTERVAL FOR MEDIAN ACHIEVED N MEDIAN CONFIDENCE CONFIDENCE INTERVAL POSITION C3 20 3.000 0.8847 ( 2.000, 3.000) 7 0.9500 ( 1.235, 3.000) NLI 0.9586 ( 1.000, 3.000) 6 MTB > NOTE compare with paired t interval 90% (1.38, 3.62) MTB > stest 0 c3 SIGN TEST OF MEDIAN = 0.00000 VERSUS N.E. 0.00000 N BELOW EQUAL ABOVE P-VALUE MEDIAN C3 20 1 3 16 0.0003 3.000 MTB > cdf 15; SUBC> binomial 17 .5. K P( X LESS OR = K) 15.00 0.9999 MTB > cdf 15; SUBC> binomial 20 .5. K P( X LESS OR = K) 15.00 0.9941 MTB > sort c3 c4 MTB > print c4 C4 -6 0 0 0 1 1 2 2 2 3 3 3 3 3 3 6 6 6 6 6 MTB > wtest c3 TEST OF MEDIAN = 0.000000 VERSUS MEDIAN N.E. 0.000000 N FOR WILCOXON ESTIMATED N TEST STATISTIC P-VALUE MEDIAN C3 20 17 138.5 0.004 3.000 MTB > winterval 95 c3 ESTIMATED ACHIEVED N MEDIAN CONFIDENCE CONFIDENCE INTERVAL C3 20 3.00 95.0 ( 1.50, 4.00) NOTE *** Data Editor entered at this point. MTB > erase c1-c4 NOTE *** The Data Editor has changed the worksheet MTB > write 'a:\ed257\oxygen.dat' c1-c2 * NOTE * Column lengths not equal NOTE *** The Data Editor has changed the worksheet MTB > write 'a:\ed257\oxygen.dat' c1-c2 MTB > dotplot c1-c2; SUBC> same. . . : . . . . . : . +---------+---------+---------+---------+---------+-------C1 . . . : . : . : . +---------+---------+---------+---------+---------+-------C2 10.15 10.50 10.85 11.20 11.55 11.90 MTB > sort c1 c3 MTB > sort c2 c4 MTB > print c3 c4 ROW C3 C4 1 11.0 10.2 2 11.2 10.3 3 11.2 10.4 4 11.2 10.6 5 11.4 10.6 6 11.5 10.7 7 11.6 10.8 8 11.7 10.8 9 11.8 10.9 10 11.9 11.1 11 11.9 11.1 12 12.1 11.3 MTB > mann-whitney c1 c2 Mann-Whitney Confidence Interval and Test C1 N = 12 Median = 11.550 C2 N = 12 Median = 10.750 Point estimate for ETA1-ETA2 is 0.800 95.4 pct c.i. for ETA1-ETA2 is (0.500,1.100) W = 216.0 Test of ETA1 = ETA2 vs. ETA1 n.e. ETA2 is significant at 0.0002 The test is significant at 0.0002 (adjusted for ties) MTB > twosample c1 c2 TWOSAMPLE T FOR C1 VS C2 N MEAN STDEV SE MEAN C1 12 11.542 0.348 0.10 C2 12 10.733 0.337 0.097 95 PCT CI FOR MU C1 - MU C2: (0.52, 1.099) TTEST MU C1 = MU C2 (VS NE): T= 5.79 P=0.0000 DF= 21 MTB > Stop *** Minitab Release 7.1 *** Minitab, Inc. *** Storage available 16179