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Diffstat (limited to '331/CH9/EX9.19/Example_9_19.sce')
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1 files changed, 224 insertions, 0 deletions
diff --git a/331/CH9/EX9.19/Example_9_19.sce b/331/CH9/EX9.19/Example_9_19.sce new file mode 100755 index 000000000..4cee24f24 --- /dev/null +++ b/331/CH9/EX9.19/Example_9_19.sce @@ -0,0 +1,224 @@ +//Caption:Mann-Whitney U Test
+//Example9.19
+//Page342
+//Ho: Two samples are drawn from different populations having the same distribution
+//H1: The mean performance ratings of the programmers from the population of the
+//Branch-1 is stochastically larger than that of the programmers from the population
+//of the Branch-2
+//Rule for decision making: If the calculated ZU is more than Zalpha, then reject Ho
+//otherwise accept Ho
+
+clc;
+X1 = [87,76,57,50,43,73,40,90,75,85,91,68,73,79,59,50,35,82,73,66];//Performance indices of branch-1
+X2 = [78,55,92,71,25,62,45,77,34,50,83,97,53,89,74,30,54,32];//performance indices of branch-2
+X= [X1,X2];//
+n1 = length(X1);
+n2 = length(X2);
+N = length(X);
+[X_sort,ind] = gsort(X,'g','i');
+disp(ind,'Rank:');
+disp(X_sort,'Index:')
+j = 1;
+for i = 1:N
+ R(i)=i;
+ if (i~=N) then
+ if (X_sort(i)==X_sort(i+1)) then
+ K(j)=i;
+ j = j+1;
+ elseif (i>1)&(X_sort(i)==X_sort(i-1))
+ K(j)= i;
+ j = j+1;
+ end
+ end
+end
+for i = 1:length(K)
+ if (i<=floor(length(K)/2)) then
+ R(K(i))= sum(K([1:floor(length(K)/2)]))/floor(length(K)/2);
+ elseif(i>floor(length(K)/2))
+ R(K(i))= sum(K([floor(length(K)/2)+1:length(K)]))/floor(length(K)/2);
+ end
+end
+disp(R,'Revised Rank')
+for i =1:N
+ for j= 1:n1
+ if(X_sort(i)==X1(j))
+ R_S1(j) = R(i);
+ elseif (j<=n2)&(X_sort(i)==X2(j))
+ R_S2(j) = R(i);
+ end
+ end
+end
+R_S1 = gsort(R_S1,'g','i');
+disp(R_S1,'Ranks of Sample-1=');
+R_S2 = gsort(R_S2,'g','i');
+disp(R_S2,'Ranks of Sample-2=');
+Sum_R_S1 = sum(R_S1);
+disp(Sum_R_S1,'The sum of the ranks of the sample-1')
+Sum_R_S2 = sum(R_S2);
+disp(Sum_R_S2,'The sum of the ranks of the sample-2')
+U = n1*n2+(n1*(n1+1)/2)-Sum_R_S1;
+disp(U,'U=')
+uU = n1*n2/2; //mean
+disp(uU,'Mean uU=')
+sigU = n1*n2*(n1+n2+1)/12; //variance
+disp(sigU,'variance =')
+Std = sqrt(sigU);
+disp(Std,'Standard Deviation=')
+ZU = (U-uU)/Std;
+alpha = 0.05;//significance level
+Z_stand = standard_normal_zstat(alpha);
+disp(ZU,'Calculated Z statistic ZU=')
+disp(Z_stand,'Standard normal z statistic Z_Stand=')
+if (ZU < Z_stand)
+ disp('Since the computed ZU is less than Zalpha, accept the Null hypothesis')
+else
+ disp('Reject the Null hypothesis')
+end
+//Result
+// Rank:
+// column 1 to 17
+//
+// 25. 36. 38. 29. 17. 7. 5. 27. 4. 16. 30. 33. 37. 22. 3. 15. 26.
+//
+// column 18 to 34
+//
+// 20. 12. 24. 6. 13. 19. 35. 9. 2. 28. 21. 14. 18. 31. 10. 1. 34.
+//
+// column 35 to 38
+//
+// 8. 11. 23. 32.
+//
+// Index:
+//
+//
+// column 1 to 17
+//
+// 25. 30. 32. 34. 35. 40. 43. 45. 50. 50. 50. 53. 54. 55. 57. 59. 62.
+//
+// column 18 to 34
+//
+// 66. 68. 71. 73. 73. 73. 74. 75. 76. 77. 78. 79. 82. 83. 85. 87. 89.
+//
+// column 35 to 38
+//
+// 90. 91. 92. 97.
+//
+// Revised Rank
+//
+// 1.
+// 2.
+// 3.
+// 4.
+// 5.
+// 6.
+// 7.
+// 8.
+// 10.
+// 10.
+// 10.
+// 12.
+// 13.
+// 14.
+// 15.
+// 16.
+// 17.
+// 18.
+// 19.
+// 20.
+// 22.
+// 22.
+// 22.
+// 24.
+// 25.
+// 26.
+// 27.
+// 28.
+// 29.
+// 30.
+// 31.
+// 32.
+// 33.
+// 34.
+// 35.
+// 36.
+// 37.
+// 38.
+//
+// Ranks of Sample-1=
+//
+// 5.
+// 6.
+// 7.
+// 10.
+// 10.
+// 15.
+// 16.
+// 18.
+// 19.
+// 22.
+// 22.
+// 22.
+// 25.
+// 26.
+// 29.
+// 30.
+// 32.
+// 33.
+// 35.
+// 36.
+//
+// Ranks of Sample-2=
+//
+// 1.
+// 2.
+// 3.
+// 4.
+// 8.
+// 10.
+// 12.
+// 13.
+// 14.
+// 17.
+// 20.
+// 24.
+// 27.
+// 28.
+// 31.
+// 34.
+// 37.
+// 38.
+//
+// The sum of the ranks of the sample-1
+//
+// 418.
+//
+// The sum of the ranks of the sample-2
+//
+// 323.
+//
+// U=
+//
+// 152.
+//
+// Mean uU=
+//
+// 180.
+//
+// variance =
+//
+// 1170.
+//
+// Standard Deviation=
+//
+// 34.205263
+//
+// Calculated Z statistic ZU=
+//
+// - 0.8185875
+//
+// Standard normal z statistic Z_Stand=
+//
+// 1.64
+//
+// Since the computed ZU is less than Zalpha, accept the Null hypothesis
+
\ No newline at end of file |