1. Below

are the scores collected from two tests that measure verbal ability

Individual

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Test 1

Test 2

1

55

94

2

52

91

3

51

88

4

48

84

5

44

86

6

40

81

7

37

85

8

34

76

9

32

79

10

30

74

a. Draw a

scatterplot for the data

b. Compute

the Pearson correlation coefficient

c. Interpret

the Pearson correlation coefficient

+ this attachment sheet Correlation Coefficient and Determination I(1).pdf

correlation_coefficient_and_determination_i_1_.pdf

Unformatted Attachment Preview

Exercise 28 Alcohol Consumption and Related Variables

Correlation Coefficient and Coefficient of Determination: I

Statistical Guide

To review correlation coefficients, see the Statistical Guide for Exercise 25.

The coefficient of determination is r squared; its symbol is r 2. For instance, if r = .50, then, r2

= .50 x .50 = .25. Multiplying this result by 100 yields the explained variance (also known as the

amount of variance accounted for) expressed as a percentage. In this example, the explained variance expressed as a percentage is .25 x 100 = 25%. This indicates that a Pearson r of .50 represents a

relationship that is 25% higher than a Pearson r of 0.00 (that is, it is 25% better than no relationship).

It is important to notice that a Pearson r of .50 is not 50%. The coefficient of determination must be

used to determine the correct percentage for interpreting the value of Pearson r.

The interpretation of a coefficient of determination for a negative value of r is the same as for

a positive value except that it applies to an inverse relationship. For instance, .16 (a positive value) is

the coefficient of determination for an r of —.40 (a negative value). Multiplying by 100, we learn that

a value of —.40 is 16% away from 0.00 in the negative direction. Coefficients of determination are

always positive because of the squaring. Hence, we use positive values of the coefficient of determination to interpret both positive and negative values of r.

Excerpt from the Research Article’

Participants were 23 older adults (16 men and 7 women)…. The majority of these individuals

were in high-level corporate management positions.

The CES-D is a 20-item questionnaire designed to measure levels of depression….

The Fat Intake Scale (FIS) is a brief dietary questionnaire….

Alcohol consumption. Alcohol consumption for each participant was computed by multiplying quantity (drinks per occasion) by frequency (drinking days per week). Self-reported levels of

tension/anxiety were significantly negatively correlated with alcohol consumption (r = —.45), suggesting an inverse relationship between tension/anxiety and alcohol consumption. Neither depression

nor any of the anger scores were correlated with alcohol consumption.

Saturated fat intake. Scores on the CES-D correlated with scores on the FIS (r = .68), sugesting a direct and positive relationship between level of depression and saturated fat intake. Scores

n the Trait-Anger scale and the Anger Expression scale were also correlated with the FIS (r = .51

d .52, respectively), also suggesting a direct and positive relationship between level of trait anger

d external anger expression with saturated fat intake.

Exercise: Aerobic and strength training. Scores on the Trait-Anger scale were significantly

egatively correlated with the self-reported level of aerobic exercise (r = —.44), suggesting an inerse relationship between level of trait anger and level of aerobic exercise. Scores on Anger Exession were, however, positively correlated with self-reported level of strength training (r = .51),

gesting a strong positive relationship between level of internal anger expression and engagement

strength training.

ce: Anton, S. D., & Miller, P. M. (2005). Do negative emotions predict alcohol consumption, saturated fat intake,

hysical activity in older adults? Behavior Modification, 29, 677-688.

81

Exercise 28 Alcohol Consumption and Related Variables: Correlation Coefficient and Coefficient of Determination: I

Questions for Exercise 28

Part A: Factual Questions

1. Is the relationship between levels of tension/anxiety and alcohol consumption direct or inverse?

2. The Pearson r for the relationship between CES-D depression scores and FIS fat intake scores

indicates that

A. higher depression is associated with less fat intake.

B. higher depression is associated with more fat intake.

3. What is the value of the coefficient of determination for the relationship between tension/anxiety

and alcohol consumption? Explain how you computed the answer.

4. What is the value of the coefficient of determination for the relationship between CES—D scores

and FIS scores? Explain how you computed the answer.

5. What is the value of the coefficient of determination for the relationship between Anger Expression scores and levels of strength training scores? Explain how you computed the answer.

6. The correlation coefficient for the relationship between Anger Expression scores and FIS scores

is .52. What percentage of the variance for Anger Expression is explained by the variance for

FIS? Explain how you computed the answer.

7. What percentage of the variance for alcohol consumption is predicted by the variance for tension/anxiety? Explain how you computed the answer.

8. In the excerpt, six correlation coefficients are reported. For which correlation coefficient is the

associated coefficient of determination highest?

82

Exercise 28 Alcohol Consumption and Related Variables: Correlation Coefficient and Coefficient of Determination: I

9. In the excerpt, six correlation coefficients are reported. For which correlation coefficient is the

associated coefficient of determination lowest?

Part B: Questions for Discussion

10.Does it surprise you that there is a direct relationship between depression and fat intake?

Explain.

11. Consider the correlation coefficient of .68 for the relationship between CES-D and FIS. Would

you characterize the relationship as being strong? Explain.

12.Consider the correlation coefficient of .68 for the relationship between CES-D and FIS. Then,

consider the corresponding percentage of explained variance. Does consideration of the percentage of explained variance influence your impression of the strength of the relationship? Explain.

83

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