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4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 11, Problem 11.10P

Textbook Problem

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Eleven neighborhoods have been rated by an urban sociologist on a “quality-of-life” scale (which includes measures of affluence, availability of medical care, and recreational facilities) and a social cohesion scale. The results are presented here in scores. Higher scores indicate higher quality of life and greater social cohesion. Are the two variables associated? What is the strength and direction of the association? Summarize the relationship in a sentence or two. *(HINT: Don forget to square the Value of Spearman’s rho for a PRE interpretation.)*

Neighborhood |
Quality of Life |
Social Cohesion |

Beaconsdale | 17 | 8.8 |

Bretwood | 40 | 3.9 |

Chesapeake Shores | 47 | 4.0 |

College Park | 90 | 3.1 |

Denbigh Plantation | 35 | 7.5 |

Kingswood | 52 | 3.5 |

North End | 23 | 6.3 |

Phoebus | 67 | 1.7 |

Riverview | 65 | 9.2 |

Queens Lake | 63 | 3.0 |

Windsor Forest | 100 | 5.3 |

To determine

**To find:**

The spearman’s rho correlation.

**Given:**

The table of eleven neighborhoods rated on urban sociologist on a quality of life scale and social cohesion is given below,

Neighborhood | Quality of Life | Social Cohesion |

Beaconsdale | 17 | 8.8 |

Bretwood | 40 | 3.9 |

Chesapeake Shores | 47 | 4.0 |

College Park | 90 | 3.1 |

Denbigh Plantation | 35 | 7.5 |

Kingswood | 52 | 3.5 |

North End | 23 | 6.3 |

Phoebus | 67 | 1.7 |

Riverview | 65 | 9.2 |

Queens Lake | 63 | 3.0 |

Windsor Forest | 100 | 5.3 |

**Formula used:**

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

Where,

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

**Calculation:**

Let the Quality of life be

Consider the following table of differences in ranks,

Quality of Life |
Social Cohesion |
Rank |
Rank |
||

17 | 8.8 | 1 | 10 | 81 | |

40 | 3.9 | 4 | 5 | 1 | |

47 | 4.0 | 5 | 6 | 1 | |

90 | 3.1 | 10 | 3 | 7 | 49 |

35 | 7.5 | 3 | 9 | 36 | |

52 | 3.5 | 6 | 4 | 2 | 4 |

23 | 6.3 | 2 | 8 | 36 | |

67 | 1.7 | 9 | 1 | 8 | 64 |

65 | 9.2 | 8 | 11 | 9 | |

63 | 3.0 | 7 | 2 | 5 | 25 |

100 | 5.3 | 11 | 7 | 4 | 16 |

Rank the highest score on each variable with 1, and so on.

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

Substitute 1 for

Essentials Of Statistics

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