Question

Speed Dating Listed on the top of the next page are attribute ratings of males by females who participated in speed dating events (from Data Set 18 “Speed Dating” in Appendix B ). In using the Kruskal-Wallis test, we must rank all of the data combined, and then we must find the sum of the ranks for each sample. Find the sum of the ranks for each of the three samples.

Age 20-22	38	42	30	39	47	43	33	31	32	28
Age 23-26	39	31	36	35	41	45	36	23	36	20
Age 27-29	36	42	35.5	27	37	34	22	47	36	32

Short answer

The sum of the ranks corresponding to the age bracket of 20-22 is equal to 164.5.

The sum of the ranks corresponding to the age bracket of 23-26 is equal to 150.

The sum of the ranks corresponding to the age bracket of 27-29 is equal to 150.5.

Step-by-step solution

Given information

Three samples are given showing the attribute ratings of people in different age groups.

Assigning ranks

The ranks of the observations from the three samples are given using the following steps:

• Combine the three samples and label each observation with the sample name/number it comes from.
• The smallest observation is assigned rank 1; the next smallest observation is assigned rank 2, and so on until the largest value.
• If two observations have the same value, the mean of the ranks is assigned to them.

The following table shows the ranks:

Attribute ratings	Sample number	Ranks
38	Sample 1	21
42	Sample 1	25.5
30	Sample 1	6
39	Sample 1	22.5
47	Sample 1	29.5
43	Sample 1	27
33	Sample 1	11
31	Sample 1	7.5
32	Sample 1	9.5
28	Sample 1	5
39	Sample 2	22.5
31	Sample 2	7.5
36	Sample 2	17
35	Sample 2	13
41	Sample 2	24
45	Sample 2	28
36	Sample 2	17
23	Sample 2	3
36	Sample 2	17
20	Sample 2	1
36	Sample 3	17
42	Sample 3	25.5
35.5	Sample 3	14
27	Sample 3	4
37	Sample 3	20
34	Sample 3	12
22	Sample 3	2
47	Sample 3	29.5
36	Sample 3	17
32	Sample 3	9.5

Calculate the sum of the ranks corresponding to the samples

The sum of the ranks corresponding to the age bracket 20-22 is computed as follows:

\(\begin{array}{c}{R_1} = 21 + 25.5 + 6 + .... + 5\\ = 164.5\end{array}\)

The sum of the ranks corresponding to the age bracket 23-26 is computed as follows:

\(\begin{array}{c}{R_2} = 22.5 + 7.5 + 17 + .... + 1\\ = 150\end{array}\)

The sum of the ranks corresponding to the age bracket 27-29 is computed as follows:

\(\begin{array}{c}{R_3} = 17 + 25.5 + 14 + .... + 9.5\\ = 150.5\end{array}\)