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

506 CHAPTER 15 | Correlation
3. What is measured by a partial correlation?
a. It is the correlation obtained for a sample with missing scores (X or Y values).
b. It is the correlation obtained for a restricted range of scores.
c. It eliminates the influence of outliers (extreme scores) when computing a
correlation.
d. It measures the relationship between two variables while controlling the influence
of a third variable.
ANSWERS
1. D, 2. B, 3. D
15.4 Hypothesis Tests with the Pearson Correlation
LEARNING OBJECTIVE
8. Conduct a hypothesis test evaluating the significance of a correlation.
The Pearson correlation is generally computed for sample data. As with most sample statistics,
however, a sample correlation is often used to answer questions about the corresponding
population correlation. For example, a psychologist would like to know whether
there is a relationship between IQ and creativity. This is a general question concerning a
population. To answer the question, a sample would be selected, and the sample data would
be used to compute the correlation value. You should recognize this process as an example
of inferential statistics: using samples to draw inferences about populations. In the past,
we have been concerned primarily with using sample means as the basis for answering
questions about population means. In this section, we examine the procedures for using a
sample correlation as the basis for testing hypotheses about the corresponding population
correlation.
■ The Hypotheses
The basic question for this hypothesis test is whether a correlation exists in the population.
The null hypothesis is “No. There is no correlation in the population.” or “The population
correlation is zero.” The alternative hypothesis is “Yes. There is a real, nonzero correlation
in the population.” Because the population correlation is traditionally represented by ρ (the
Greek letter rho), these hypotheses would be stated in symbols as
H 0
: ρ = 0
H 1
: ρ ≠ 0
(There is no population correlation.)
(There is a real correlation.)
When there is a specific prediction about the direction of the correlation, it is possible
to do a directional, or one-tailed test. For example, if a researcher is predicting a positive
relationship, the hypotheses would be
H 0
: ρ ≤ 0
H 1
: ρ > 0
(The population correlation is not positive.)
(The population correlation is positive.)
The correlation from the sample data is used to evaluate the hypotheses. For the regular,
nondirectional test, a sample correlation near zero provides support for H 0
and a sample
value far from zero tends to refute H 0
. For a directional test, a positive value for the sample
correlation would tend to refute a null hypothesis stating that the population correlation is
not positive.