If W, the Wilcoxon rank sum test statistic is the sum of the ranks assigned to t

Question

If W, the Wilcoxon rank sum test statistic is the sum of the ranks assigned to the heights of peach seedlings receiving Herbicide A, then the value of W is a. 24.5. b. 52.0. c. 53.5.

Some researchers have suggested that stem-pitting disease in peach tree seedlings can be controlled with soil treatment. An experiment was conducted to compare peach tree seedling growth with soil and weeds treated with one of two herbicides. In an experimental field containing 12 seedlings, six were randomly selected throughout the field to receive Herbicide A. The remaining six received Herbicide B. Soil and weed for each seedling were treated with the appropriate herbicide for three months, at which point the height in centimeters was recorded for each seedling. The following results were obtained. Herbicide Height (cm) A 97,93,91,91,89,87 B 91,87,84,78,74,69

Explanation / Answer

First, we put both samples together and organize it in ascending order, which is shown in the table below:

Now, that the values that are in ascending order are assigned ranks to them, taking care of assigning the average rank to values with rank ties

The sum of ranks for sample 1 is:

R1=5.5+7+9+9+11+12=53.5

and the sum of ranks of sample 2 is:

R2=1+2+3+4+5.5+9=24.5

Hence, the test statistic is R = R1 = 53.5 = Option C

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Sample Value 2 69 2 74 2 78 2 84 1 87 2 87 1 89 1 91 1 91 2 91 1 93 1 97

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