Two aptitude tests are currently being used to screen applicants for a certain p
ID: 3291648 • Letter: T
Question
Two aptitude tests are currently being used to screen applicants for a certain position within a company. The question arose as to whether the two tests are comparable, i.e., whether they yield the same results. Six applicants were selected at random to take both tests (in a random order). The following scores were recorded:
Use the Wilcoxon signed-rank test to determine whether there is a difference in scores between the two tests. Use Significance level = 0.10.
Applicant Test A Test B 1 85 87 2 93 94 3 98 92 4 68 73 5 76 73 6 83 85Explanation / Answer
Solution:-
Null Hypothesis
The null hypothesis asserts that the medians of the two samples are identical.
Alternate Hypothesis
The alternate hypothesis asserts that the medians of the two samples are not identical.
Calculation:-
W-value: 10
Mean Difference: -10.17
Sum of pos. ranks: 10
Sum of neg. ranks: 11
Z-value: -0.1048 (nb. N too small)
Sample Size (N): 6
Result 1 - Z-value
The Z-value is -0.1048. However, the size of N (6) is not large enough for the distribution of the Wilcoxon W statistic to form a normal distribution. Therefore, it is not possible to calculate an accurate p-value.
Result 2 - W-value
The W-value is 10. The critical value of W for N = 6 at p 0.10 is 0. Therefore, the result is not significant at p 0.10.
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