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S O C Following are the scores of a sample of 15 nations on a measure of ethnic diversity (the higher the number, the greater the diversity) and a measure of economic inequality (the higher the score, the greater the inequality) Are these variables related? Are ethnically diverse nations more economically unequal? Nation Diversity Inequality India 91 29.7 South Africa 87 58.4 Kenya 83 57.5 Canada 75 31.5 Malaysia 72 48.4 Kazakhstan 69 32.7 Egypt 65 32.0 United States 63 41.0 Sri Lanka 57 30.1 Mexico 50 50.3 Spain 44 32.5 Australia 31 33.7 Finland 16 25.6 Ireland 4 35.9 Poland 3 27.2

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Essentials Of Statistics

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

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Chapter
Section
BuyFindarrow_forward

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 11, Problem 11.11P
Textbook Problem
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S O C Following are the scores of a sample of 15 nations on a measure of ethnic diversity (the higher the number, the greater the diversity) and a measure of economic inequality (the higher the score, the greater the inequality) Are these variables related? Are ethnically diverse nations more economically unequal?

Nation Diversity Inequality
India 91 29.7
South Africa 87 58.4
Kenya 83 57.5
Canada 75 31.5
Malaysia 72 48.4
Kazakhstan 69 32.7
Egypt 65 32.0
United States 63 41.0
Sri Lanka 57 30.1
Mexico 50 50.3
Spain 44 32.5
Australia 31 33.7
Finland 16 25.6
Ireland 4 35.9
Poland 3 27.2

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,

Nation Diversity Inequality
India 91 29.7
South Africa 87 58.4
Kenya 83 57.5
Canada 75 31.5
Malaysia 72 48.4
Kazakhstan 69 32.7
Egypt 65 32.0
United States 63 41.0
Sri Lanka 57 30.1
Mexico 50 50.3
Spain 44 32.5
Australia 31 33.7
Finland 16 25.6
Ireland 4 35.9
Poland 3 27.2

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,

Diversity (X) Inequality (Y) Rank (X) Rank (Y) D D2
91 29.7 1 13 144
87 58.4 2 1 1 1
83 57.5 3 2 1 1
75 31.5 4 11 49
72 48.4 5 4 1 1
69 32.7 6 8 4
65 32.0 7 10 9
63 41.0 8 5 3 9
57 30.1 9 12 9
50 50.3 10 3 7 49
44 32.5 11 9 2 4
31 33.7 12 7 5 25
16 25.6 13 15 4
4 35.9 14 6 8 64
3 27.2 15 14 1 1
D=0

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