   # S W A sample of children has been observed and rated for symptoms of depression. Their parents have been rated for level of alcohol use. Is there any relationship between these variables? Write a few sentences stating your conclusions. Symptoms of Depression Level of Alcohol Use Low Moderate High Totals Few 7 8 9 24 Some 15 10 18 43 Many Totals 8 30 12 30 3 30 23 90 ### Essentials Of Statistics

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

#### Solutions

Chapter
Section ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 11, Problem 11.9P
Textbook Problem
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## S W A sample of children has been observed and rated for symptoms of depression. Their parents have been rated for level of alcohol use. Is there any relationship between these variables? Write a few sentences stating your conclusions. Symptoms of Depression Level of Alcohol Use Low Moderate High Totals Few 7 8 9 24 Some 15 10 18 43 ManyTotals 8 30 12 30 3 30 23 90

To determine

To find:

The strength and pattern of relationship.

### Explanation of Solution

Given:

The given statement is,

A sample of children has been observed and rated for symptoms of depression. Their parents have been rated for level of alcohol use.

The given table of information is,

 Symptoms of Depression Level of Alcohol Use Low Moderate High Totals Few 7 8 9 24 Some 15 10 18 43 Many 8 12 3 23 Totals 30 30 30 90

Approach:

If the gamma value is less than 0.30, it is said that there is a weak association between the categories.

If the gamma value is greater than 0.60, it is said that there is a strong association between the categories.

The gamma compares the number of pairs of cases ranked in the same order on both variables (Ns) with the number of cases ranked in different order (Nd).

Formula used:

For compares the number of pairs of cases ranked in the same order on both variables (Ns) with the number of cases ranked in different order (Nd) the gamma G is given as,

G=NsNdNs+Nd

Calculation:

From the given table of information,

The value of Ns is computed as,

Ns=7(10+18+12+3)+8(18+3)+15(12+3)+10(3)=724

And the value of Nd is computed as,

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