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a. State the null hypothesis
Ho: The two samples are identical
b. State the alternative hypothesis
Ha: The two samples are...
d. Rank the absolute values of these
differences, giving the smallest
difference rank 1 and assigning
average ranks to tie...
g. Find the smaller of the absolute
values of the two sums of the ranks
and denote it by T.

h. Test Ho by comparing T wit...
A research team subjected to a sensory evaluation test a camote rops
extract (CTE) beverage by comparing it to a commercia...
•Ho: CTE and GTD are identical.
•HA: CTE and GTD are not identical.
•Get the differences (D) between paired values. Rank t...
Wilcoxon Signed Rank Test
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Wilcoxon Signed Rank Test

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Wilcoxon signed rank test for a paired experiment

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Wilcoxon Signed Rank Test

  1. 1. a. State the null hypothesis Ho: The two samples are identical b. State the alternative hypothesis Ha: The two samples are not identical c. Obtain the differences between paired values in the two samples/treatments.
  2. 2. d. Rank the absolute values of these differences, giving the smallest difference rank 1 and assigning average ranks to tied differences. e. Assign to each rank the sign of the observed differences. f. Get the sum of the positive ranks and the sum of the negative ranks.
  3. 3. g. Find the smaller of the absolute values of the two sums of the ranks and denote it by T. h. Test Ho by comparing T with the critical values of T for the Wilcoxon Signed Rank Test found in the appendix. i. If T is less than or equal to Tcritical for the chosen level of significance, α, then the null hypothesis is rejected. Otherwise the null hypothesis is not
  4. 4. A research team subjected to a sensory evaluation test a camote rops extract (CTE) beverage by comparing it to a commercially available green tea drink (GTD) in terms of acceptability of the product. The drinks were ranked from 1 (lower rank) to 10 (highest rank). The following data were obtained. Evaluator CTE GTD Evaluator CTE GTD 1 7 9 9 8 9 2 2 3 10 1 2 3 5 2 11 3 2 4 4 1 12 6 3 5 6 5 13 9 7 6 1 1 14 3 5 7 5 4 15 4 1 8 6 4 16 6 5 Test the Ho which states that CTE and GTD are identical in terms of acceptability.
  5. 5. •Ho: CTE and GTD are identical. •HA: CTE and GTD are not identical. •Get the differences (D) between paired values. Rank the absolute values of D. Evaluator 1 2 3 4 5 6 7 8 R= -36 D -2 -1 3 3 1 0 1 2 R= 100 Rank 10.5 -5 14.5 14.5 5 1 5 10.5 Evaluator 9 10 11 12 13 14 15 16 D -1 -1 1 3 2 -2 3 1 T= 36 •Test the null hypothesis by comparing the value of T= 36 with Tcritical= 30 at α= 0.05. •Decision: Since T > Tcritical, the null hypothesis is not rejected. It means that the two treatments are identical. Rank -5 -5 5 14.5 10.5 -10.5 14.5 5

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