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Twenty ethnic, racial, or national groups were rated by a random sample of white and black students on a Social Distance Scale. Lower scores represent less social distance and less prejudice. How similar are these rankings? Average Score Group White Students Black Students 1 White Americans 1.2 2.6 2 English 1.4 2.9 3 Canadians 1.5 3.6 4 Irish 1.6 3.6 5 Germans 1.8 3.9 6Italians 1.9 3.3 7 Norwegians 2.0 3.8 8 American Indians 2.1 2.7 9 Spanish 2.2 3.0 10 Jews 2.3 3.3 11 Poles 2.4 4.2 12 Black Americans 2.4 1.3 13 Japanese 2.8 3.5 14 Mexicans 2.9 3.4 15 Koreans 3.4 3.7 16 Russians 3.7 5.1 17 Arabs 3.9 3.9 18 Vietnamese 3.9 4.1 19 Turks 4.2 4.4 20 Iranians 5.3 5.4

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Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

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Section
BuyFindarrow_forward

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 11, Problem 11.12P
Textbook Problem
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Twenty ethnic, racial, or national groups were rated by a random sample of white and black students on a Social Distance Scale. Lower scores represent less social distance and less prejudice. How similar are these rankings?

Average Score
Group White Students Black Students
1 White Americans 1.2 2.6
2 English 1.4 2.9
3 Canadians 1.5 3.6
4 Irish 1.6 3.6
5 Germans 1.8 3.9
6Italians 1.9 3.3
7 Norwegians 2.0 3.8
8 American Indians 2.1 2.7
9 Spanish 2.2 3.0
10 Jews 2.3 3.3
11 Poles 2.4 4.2
12 Black Americans 2.4 1.3
13 Japanese 2.8 3.5
14 Mexicans 2.9 3.4
15 Koreans 3.4 3.7
16 Russians 3.7 5.1
17 Arabs 3.9 3.9
18 Vietnamese 3.9 4.1
19 Turks 4.2 4.4
20 Iranians 5.3 5.4

To determine

To find:

The spearman’s rho correlation.

Explanation of Solution

Given:

The table of 15 nations on a measure of ethnic diversity and economic inequality is given below,

Average Score
Group White Students Black Students
1 White Americans 1.2 2.6
2 English 1.4 2.9
3 Canadians 1.5 3.6
4 Irish 1.6 3.6
5 Germans 1.8 3.9
6 Italians 1.9 3.3
7 Norwegians 2.0 3.8
8 American Indians 2.1 2.7
9 Spanish 2.2 3.0
10 Jews 2.3 3.3
11 Poles 2.4 4.2
12 Black Americans 2.4 1.3
13 Japanese 2.8 3.5
14 Mexicans 2.9 3.4
15 Koreans 3.4 3.7
16 Russians 3.7 5.1
17 Arabs 3.9 3.9
18 Vietnamese 3.9 4.1
19 Turks 4.2 4.4
20 Iranians 5.3 5.4

Formula used:

The formula to calculate the Spearman’s rho is given by,

rs=16D2N(N21)

Where, D2 is the sum of the squares of the differences in ranks, and N is the number of observations.

The formula to calculate the difference in ranks is calculated as,

D1=Rank(X1)Rank(Y1)

Calculation:

Let the Quality of life be X and social cohesion be Y.

Consider the following table of differences in ranks,

White Students (X) Black Students (Y) Rank (X) Rank (Y) D D2
1.2 2.6 20 19 1 1
1.4 2.9 19 17 2 4
1.5 3.6 18 10.5 7.5 56.25
1.6 3.6 17 10.5 6.5 42.25
1.8 3.9 16 6.5 9.5 90.25
1.9 3.3 15 14.5 0.5 0.25
2.0 3.8 14 8 6 36
2.1 2.7 13 18 5 25
2.2 3.0 12 16 4 16
2.3 3.3 11 14.5 3.5 12.25
2.4 4.2 9.5 4 5.5 30.25
2.4 1.3 9.5 20 10.5 110.25
2.8 3.5 8 12 4 16
2.9 3.4 7 13 6 36
3.4 3.7 6 9 3 9
3.7 5.1 5 2 3 9
3.9 3.9 3.5 6.5 3 9
3

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