Question

Wilcoxon Rank-Sum Test

Is there a difference between Girls and Boys on number of books read?

Boys 12, 5, 13, 3, 11

Girls 4, 10, 9, 7, 6

Answer 1

Hello Sir/ Mam

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

Sample	Value
1	3
2	4
1	5
2	6
2	7
2	9
2	10
1	11
1	12
1	13

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

Sample	Value	Rank	Rank (Adjusted for ties)
1	3	1	1
2	4	2	2
1	5	3	3
2	6	4	4
2	7	5	5
2	9	6	6
2	10	7	7
1	11	8	8
1	12	9	9
1	13	10	10

The sum of ranks for sample 1 is:

R₁ = 1+3+8+9+10 = 31

and the sum of ranks of sample 2 is:

R₂ = 2+4+5+6+7 = 24

Hence, the test statistic is R = R₁ = 31.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H₀​: Median (Difference) = 0

H_a​: Median (Difference) ≠ 0

(2) Rejection Region

The critical value for the signficance level provided and the type of tail is R_c = 8, and the null hypothesis is rejected if R ≤ 8.

(3) Decision about the null hypothesis

Since in this case R = 31 > 8, there is not enough evidence to claim that the population median of differences is different than 0, at the 0.05 significance level.

I hope this solves your doubt.

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