To get started, type one of these: helpwin, helpdesk, or demo. For product information, visit www.mathworks.com. Water Diffusion across human chorioaminon tissue X: At term (approx 39weeks, Control) Y: 12-26 weeks Data from textbook Table 4.1 p110 (2nd edn) Use Wilcoxon Rank-Sum-test procedures for two samples: X (m=10): 0.80 0.83 1.89 1.04 1.45 1.38 1.91 1.64 0.73 1.46 Y (n= 5): 1.15 0.88 0.90 0.74 1.21 SampleSizes_X_Y_Both = 10 5 15 Columns are Ordinal, Group number, and Values: dd = 1.0000 1.0000 0.8000 2.0000 1.0000 0.8300 3.0000 1.0000 1.8900 4.0000 1.0000 1.0400 5.0000 1.0000 1.4500 6.0000 1.0000 1.3800 7.0000 1.0000 1.9100 8.0000 1.0000 1.6400 9.0000 1.0000 0.7300 10.0000 1.0000 1.4600 11.0000 2.0000 1.1500 12.0000 2.0000 0.8800 13.0000 2.0000 0.9000 14.0000 2.0000 0.7400 15.0000 2.0000 1.2100 Tie-group sizes for tie-groups with more than one value: Number_of_Tie_Groups = 0 Columns are Ordinal, Group numbers, Values, and Midranks: (The function getmidranks() was used to generate midranks.) Note: Could use fprintf() to suppress unnecessary 0s dd = 1.0000 1.0000 0.8000 3.0000 2.0000 1.0000 0.8300 4.0000 3.0000 1.0000 1.8900 14.0000 4.0000 1.0000 1.0400 7.0000 5.0000 1.0000 1.4500 11.0000 6.0000 1.0000 1.3800 10.0000 7.0000 1.0000 1.9100 15.0000 8.0000 1.0000 1.6400 13.0000 9.0000 1.0000 0.7300 1.0000 10.0000 1.0000 1.4600 12.0000 11.0000 2.0000 1.1500 8.0000 12.0000 2.0000 0.8800 5.0000 13.0000 2.0000 0.9000 6.0000 14.0000 2.0000 0.7400 2.0000 15.0000 2.0000 1.2100 9.0000 Data sorted by Z-value to show midranks and any tie groups (Sorted on Z-value then Group number then Ordinal as tie-breakers) Columns are Ordinal, Group number, Value, and Midrank Using fprintf rather than matrix display for variety 9. 1 0.73 1.0 14. 2 0.74 2.0 1. 1 0.80 3.0 2. 1 0.83 4.0 12. 2 0.88 5.0 13. 2 0.90 6.0 4. 1 1.04 7.0 11. 2 1.15 8.0 15. 2 1.21 9.0 6. 1 1.38 10.0 5. 1 1.45 11.0 10. 1 1.46 12.0 8. 1 1.64 13.0 3. 1 1.89 14.0 7. 1 1.91 15.0 WILCOXON RANK SUM SCORES: (Since the treatment group (Y) is smaller, we show its score first) Yscore: Observed: 30.00 Expected: 40.00 Xscore: Observed: 90.00 Expected: 80.00 Score-Expected in both cases: -10.00 ASSUMING THAT THERE ARE NO TIES (See WcxRankSum2.m for handling of ties) Wstd_Zval_Pval_NOTIECORR = 8.1650 -1.2247 0.2207 SIMULATING THE TRUE Wilcoxon Rank-Sum P-VALUE: Using NSIMS random permutations: Nsims = 10000 INITIALIZING the random-number generator at Wseed = 2.0857e+005 ASSUMING ObsWscoreY is on the LOWER TAIL: (That is, ObsWscoreY should be LESS than WExpScY) ObsWscoreY_ExpWscoreY = 30 40 SIMULATED value for true 2-sided P-value: NLessEq=1292 Nsims=10000 Pvalue=0.25840 (2-sided) 95%% Confidence Interval for true P-value (with Estimate in middle): Plow_PEst_Phigh = 0.2453 0.2584 0.2715 The Hodges-Lehmann estimator for theta for Y=X+theta is the median of the Mann-Whitney differences W_k=Y_i-X_j: Mann-Whitney differences (n=15, nmwd=50, nrows=5): 0.35 0.08 0.10 -0.06 0.41 0.32 0.05 0.07 -0.09 0.38 -0.74 -1.01 -0.99 -1.15 -0.68 0.11 -0.16 -0.14 -0.30 0.17 -0.30 -0.57 -0.55 -0.71 -0.24 -0.23 -0.50 -0.48 -0.64 -0.17 -0.76 -1.03 -1.01 -1.17 -0.70 -0.49 -0.76 -0.74 -0.90 -0.43 0.42 0.15 0.17 0.01 0.48 -0.31 -0.58 -0.56 -0.72 -0.25 SORTED M-W differences (n=15, nmwd=50, nrows=5): ( 1) -1.17 -1.15 -1.03 -1.01 -1.01 -0.99 -0.90 -0.76 -0.76 -0.74 ( 11) -0.74 -0.72 -0.71 -0.70 -0.68 -0.64 -0.58 -0.57 -0.56 -0.55 ( 21) -0.50 -0.49 -0.48 -0.43 -0.31 -0.30 -0.30 -0.25 -0.24 -0.23 ( 31) -0.17 -0.16 -0.14 -0.09 -0.06 0.01 0.05 0.07 0.08 0.10 ( 41) 0.11 0.15 0.17 0.17 0.32 0.35 0.38 0.41 0.42 0.48 YXmeandiff_MWMedian = -0.3370 -0.3050 Normal confidence intervals for theta (Mean diff=-0.337): (-0.748, 0.074) 95% CI (-0.877, 0.203) 95% CI EXACT NONPARAMETRIC CIs for theta=med(Y)-med(X) based on the Wilcoxon rank-sum statistic: Table A6 for n=5 m=10 (MaxScore=65) has: P(W_Y ge 61)=0.004 P(W_Y ge 60)=0.006 P(W_Y ge 59)=0.010 P(W_Y ge 58)=0.014 P(W_Y ge 57)=0.020 P(W_Y ge 56)=0.028 With corresponding Mann-Whitney scores: P(W_Y ge 61) = P(MW_Y ge 46) = 0.004 P(W_Y ge 60) = P(MW_Y ge 45) = 0.006 P(W_Y ge 59) = P(MW_Y ge 44) = 0.010 P(W_Y ge 58) = P(MW_Y ge 43) = 0.014 P(W_Y ge 57) = P(MW_Y ge 42) = 0.020 P(W_Y ge 56) = P(MW_Y ge 41) = 0.028 Offsets in Mann-Whitney array with coverage probabilities: Lo= 5.0 Hi=46.0 Cprob=99.20 Lo= 6.0 Hi=45.0 Cprob=98.80 Lo= 7.0 Hi=44.0 Cprob=98.00 Lo= 8.0 Hi=43.0 Cprob=97.20 Lo= 9.0 Hi=42.0 Cprob=96.00 Lo=10.0 Hi=41.0 Cprob=94.40 Exact symmetric confidence intervals for theta: (-1.010, 0.350) 99.2% CI (-0.990, 0.320) 98.8% CI (-0.900, 0.170) 98.0% CI (-0.760, 0.170) 97.2% CI (-0.760, 0.150) 96.0% CI (-0.740, 0.110) 94.4% CI