Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 15.3 | Using and Interpreting the Pearson Correlation 495
3. A set of n = 15 pairs of X and Y values has a Pearson correlation of r = 0.10.
If each of the X values were multiplied by 2, then what is the correlation for the
resulting data?
a. 0.10
b. –0.10
c. 0.20
d. –0.20
ANSWERS
1. B, 2. B, 3. A
15.3 Using and Interpreting the Pearson Correlation
LEARNING OBJECTIVES
5. Explain how a correlation can be influenced by a restricted range of scores or by
outliers.
6. Define the coefficient of determination and explain what it measures.
7. Explain what is measured by a partial correlation.
■ Where and Why Correlation Are Used
Although correlations have a number of different applications, a few specific examples are
presented next to give an indication of the value of this statistical measure.
1. Prediction If two variables are known to be related in some systematic way, it is
possible to use one of the variables to make accurate predictions about the other.
For example, when you applied for admission to college, you were required to
submit a great deal of personal information, including your scores on the Scholastic
Achievement Test (SAT). College officials want this information so they can
predict your chances of success in college. It has been demonstrated over several
years that SAT scores and college grade point averages are correlated. Students
who do well on the SAT tend to do well in college; students who have difficulty
with the SAT tend to have difficulty in college. Based on this relationship, college
admissions officers can make a prediction about the potential success of each
applicant. You should note that this prediction is not perfectly accurate. Not
everyone who does poorly on the SAT will have trouble in college. That is why
you also submit letters of recommendation, high school grades, and other
information with your application. The process of using relationships to make
predictions is called regression and is discussed in the next chapter.
2. Validity Suppose a psychologist develops a new test for measuring intelligence.
How could you show that this test truly measures what it claims; that is, how could
you demonstrate the validity of the test? One common technique for demonstrating
validity is to use a correlation. If the test actually measures intelligence, then the
scores on the test should be related to other measures of intelligence—for example,
standardized IQ tests, performance on learning tasks, problem-solving ability, and
so on. The psychologist could measure the correlation between the new test and
each of these other measures of intelligence to demonstrate that the new test is valid.
3. Reliability In addition to evaluating the validity of a measurement procedure,
correlations are used to determine reliability. A measurement procedure is considered