# EXERCISE 19_ CORRELATION COEFFICIENT by hcj

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EXERCISE 19: CORRELATION COEFFICIENT

Relationships Among Social Variables

Statistical Guide
A correlation coefficient indicates the strength and direction of a relationship between two
variables. The most popular correlation coefficient is the Pearson r. When it is positive in value,
the relationship is direct (that is, those with high scores on one variable tend to have high scores
on the other variable and those with low scores on one variable tend to have Iow scores on the
other). In a direct relationship, the closer r is to 1.00, the stronger the relationship; the closer it is
to 0.00, the weaker the relationship.
When the value of the Pearson r is negative, the relationship is inverse (that is, those with
high scores on one variable tend to have low scores on the other one). In an inverse relationship,
the closer r is to -1.00, the stronger the relationship; the closer it is to 0.00, the weaker the
relationship.

Background Notes
Aggression and withdrawal were measured by showing a picture of all classmates and
asking each student to choose two classmates who best fit each descriptor. For aggression, a
score was obtained for each child by summing the number of times he or she was selected for
these descriptors: "gets into lots of fights," "loses temper easily, .... too bossy," and "picks on
other kids." For withdrawal, a score was obtained for each child by summing the number of
times he or she was selected for these descriptors: "rather play alone than with others" and "very
shy."
Social preference was assessed by asking each child to name three other children they would
like most and like least for playing together, inviting others to a birthday party, and sitting next
to each other on a bus. [Responses were scored in such a way that higher scores indicate greater
social preference.]
Victimization by peers was measured by asking each child to nominate up to five other
students who could be described as being made fun of, being called names, and getting hit and
pushed by other kids. [Higher scores indicate greater victimization.]
Number of affiliative links was measured by asking "You have probably noticed children in
your class who often hang around together and others who are more often alone. Could you
name the children who often hang around together?" [Higher scores indicate a larger number of
Loneliness was measured with a 16-item questionnaire with higher scores indicating greater
loneliness.
Perceived social acceptance and behavior-conflict were two aspects of self-concept measured
with Harter's Self-Perception Profile for Children, which is a questionnaire. Higher scores reflect
a better self-concept in each of the two domains.

Excerpt from the Research Article
French Canadian children (393 girls, 400 boys; mean age = 115 months, range 8 to 10 years)
participated in the study. The children attended third (n = 315), fourth (n = 248), and fifth (n =
230) grades in 10 elementary schools from a variety of socioeconomic backgrounds...
Table 1 presents the correlations among the measures considered in the present study.
Part A: Factual Questions

2. What is the value of the Pearson r for the relationship between loneliness and perceived social
acceptance? Is that relationship direct or inverse? Explain the basis for your answer.

5. Which variable has the strongest relationship with withdrawal? Explain.

7. The Pearson r for the relationship between withdrawal and loneliness indicates that those who
tend to be more lonely tend to be (A) more withdrawn or (B) less withdrawn.

8. Which of the following pairs of variables has the strongest relationship between them?
A. Perceived social acceptance and loneliness
B. Withdrawal and victimization by peers
C. Number of affiliative links and aggression

Part B. Questions for Discussion

10. In words (without using numbers), how would you describe the strength and direction of the
relationship between withdrawal and aggression?

12. In your opinion, does it make sense that the Pearson r for the relationship between loneliness
and perceived social acceptance is -.69? Explain.

13. In your opinion, does the Pearson r of-.27 for the relationship between withdrawal and
perceived social acceptance prove that being withdrawn causes less perceived social acceptance?
Explain.

Exercise from: Holcomb, Z C. (1998). Interpreting Basic Statistics (2nd Ed.). LA: Pyrczak Publ.
Source: Boivin, M., & Hymel, S. (1997). Peer experiences and social self-perceptions: A
sequential model. Developmental Psychology, 33, 135-143.

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