Testing for Relationships
Among Variables
To find whether there are relationships among variables, a variety of statistical
tests is used to determine the significance of correlations (see Table 13-12).
Decisions about which statistical tests to use are based on whether there are two
variables or more than two variables. Consideration is also given to the level
of measurement used. Understanding how decisions are made allows nurses
to ascertain the quality of the findings.Pearson’s r
When researchers pose hypotheses about the relationships among variables,
they are testing for the significance of the correlation coefficient. When
two variables are measured at the interval or ratio level, they calculate the
Pearson’s r statistic, also known as the Pearson product–moment correla-
tion (Hayes, 1994; Plichta & Kelvin, 2013). The degrees of freedom for this
test are always N − 2, which means that the correlation coefficient can be
affected by the sample size. It is possible for a small correlation coefficient
to be statistically significant when there is a large sample. In the literature,
the notation r = .62, p < .01 is used. This notation provides three important
pieces of information about the two variables. First, the variables are related
at a magnitude of .62, which is usually considered to be a moderate—or
moderately strong—relationship. Second, the two variables have a positive
relationship with each other because the value is positive. Third, the corre-
lation is statistically significant. A statistically significant correlation is one
that is significantly different from zero.
Small correlations can be statistically significant because it does not take much
variation to be significantly different from a correlation of zero (Nieswiadomy,
2012). Therefore, researchers can use a variation of Pearson’s r that determines
the percentage of variance shared by two variables, which provides more
meaningful information. By squaring the coefficient (r^2 ), the overlap, or shared
variance, is computed. A helpful way to think about variance is to think of a
pie chart. The entire pie chart represents all the variables that can contribute to
changes in the dependent variable. Each r^2 indicates how large a section of the
pie chart that variable earns. With this information, knowledge of one variable
can be used to predict the value of the other variable. For example, suppose
that a correlation coefficient of .23 was obtained for the variables self-esteem
and weight gain. Squaring .23 equals .0529. This is interpreted to mean that
self-esteem accounts for about 5% of weight gain. Thus, the researcher would
know that other variables must also contribute to weight gain.KEY TERM
Pearson’s r: An
inferential statistic
used when two
variables are
measured at the
interval or ratio
level; Pearson
product–moment
correlation368 CHAPTER 13 What Do the Quantitative Data Mean?