This chapter is concerned with measures of
*relatedness* between two variables. A simple measure,
the *correlation coefficient*, is commonly used to
quantify the degree of *association* between two
variables. Often, correlations are used during an exploratory or
observational stage of research to determine which variables *at
least* have a statistical relationship with each other. In
experimental designs, correlations are also used to determine the degree
of association between independent and dependent (or response) variables.
However, the finding of a correlation between two variables does not imply
that a change in one variable causes a corresponding change in
another—that’s why you still need experiments. Indeed, the history of
computing correlation coefficients at large, and often without any
theoretical or model-based justification, has led to numerous errors in
inference being made. In this chapter, you will learn about measures of
association, such as Pearson’s correlation coefficient, the Spearman
rank-order coefficient, the point-biserial correlation coefficient, and
phi, and review examples of the appropriate use of each. The key message
is that correlations are useful tools, but many variables in nature are
correlated; such relationships are not always useful for
inference.

The world is awash with correlations, or statistical associations between two (or more) variables. Often, such relationships are useful to characterize ...

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