Question

Listed in the accompanying data table are birth weights​ (g) from a sample of 26 births. When applying the Wilcoxon​ rank-sum test, what is the sum of the ranks for the sample of birth weights of​ girls? Girl 3700 1000 2200 4300 3100 1900 2700 3400 2900 2500 4000 3400 2700 3200 Boy 3600 2700 3700 4200 3600 1800 3400 3800 2700 3300 3400 300

The sum of the ranks for the sample of birth weights of girls is? .

Answer 1

The answer is 174.5

Let girls be Sample 1 and boys be Sample 2.

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

Sample	Value
2	300
1	1000
2	1800
1	1900
1	2200
1	2500
1	2700
1	2700
2	2700
2	2700
1	2900
1	3100
1	3200
2	3300
1	3400
1	3400
2	3400
2	3400
2	3600
2	3600
1	3700
2	3700
2	3800
1	4000
2	4200
1	4300

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)
2	300	1	1
1	1000	2	2
2	1800	3	3
1	1900	4	4
1	2200	5	5
1	2500	6	6
1	2700	7	8.5
1	2700	8	8.5
2	2700	9	8.5
2	2700	10	8.5
1	2900	11	11
1	3100	12	12
1	3200	13	13
2	3300	14	14
1	3400	15	16.5
1	3400	16	16.5
2	3400	17	16.5
2	3400	18	16.5
2	3600	19	19.5
2	3600	20	19.5
1	3700	21	21.5
2	3700	22	21.5
2	3800	23	23
1	4000	24	24
2	4200	25	25
1	4300	26	26

The sum of ranks for sample 1 i.e. girls is:

and the sum of ranks of sample 2 is: