THEPEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT(r) is only one of many avail-
able correlation coefficients. It generally applies to those situations in which the relation-
ship between two variables is basically linear, where both variables are measured on a more
or less continuous scale, and where some sort of normality and homogeneity of variance
assumptions can be made. As this chapter will point out, r can be meaningfully interpreted
in other situations as well, although for those cases it is given a different name and it is
often not recognized for what it actually is.
In this chapter we will discuss a variety of coefficients that apply to different kinds of
data. For example, the data might represent rankings, one or both of the variables might be
dichotomous, or the data might be categorical. Depending on the assumptions we are will-
ing to make about the underlying nature of our data, different coefficients will be appropri-
ate in different situations. Some of these coefficients will turn out to be calculated as if they
were Pearson rs, and some will not. The important point is that they all represent attempts
to obtain some measure of the relationship between two variables and fall under the gen-
eral heading of correlationrather than regression.
When we speak of relationships between two variables without any restriction on the
nature of these variables, we have to distinguish between correlational measuresand
measures of association.When at least some sort of order can be assigned to the levels of
each variable, such that higher scores represent more (or less) of some quantity, then it makes
sense to speak of correlation. We can speak meaningfully of increases in one variable being
associated with increases in another variable. In many situations, however, different levels of a
variable do not represent an orderly increase or decrease in some quantity. For example, we
could sort people on the basis of their membership in different campus organizations, and then
on the basis of their views on some issue. We might then find that there is in fact an associa-
tion between people’s views and their membership in organizations, and yet neither of these
variables represents an ordered continuum. In cases such as this, the coefficient we will com-
pute is not a correlation coefficient. We will instead speak of it as a measure of association.
There are three basic reasons we might be interested in calculating any type of coefficient
of correlation. The most obvious, but not necessarily the most important, reason is to obtain
an estimate of , the correlation in the population. Thus, someone interested in the validityof
a test actually cares about the true correlation between his test and some criterion, and ap-
proaches the calculation of a coefficient with this purpose in mind. This use is the one for
which the alternative techniques are least satisfactory, although they can serve this purpose.
A second use of correlation coefficients occurs with such techniques as multiple regres-
sion and factor analysis. In this situation, the coefficient is not in itself an end product;
rather, it enters into the calculation of further statistics. For these purposes, several of the
coefficients to be discussed are satisfactory.
The final reason for calculating a correlation coefficient is to use its square as a meas-
ure of the variation in one variable accountable for by variation in the other variable. This
is a measure of effect size (from the r-family of measures), and is often useful as a way of
conveying the magnitude of the effect that we found. Here again, the coefficients to be dis-
cussed are in many cases satisfactory for this purpose. I will specifically discuss the cre-
ation of r-family effect size measures in what follows.10.1 Point-Biserial Correlation and Phi: Pearson Correlations by Another Name
In the previous chapter I discussed the standard Pearson product-moment correlation coef-
ficient (r) in terms of variables that are relatively continuous on both measures. However,
that same formula also applies to a pair of variables that are dichotomous (having twor294 Chapter 10 Alternative Correlational Techniques
correlational
measures
measures of
association
validity