The basic Pearson Product
Moment Correlation Coefficient (PPMC) can be used with
several levels of measurement of both X and Y. All of the
PPMC's are algebraically equivalent and have calculated
values that range between -1.00 and 1.00. Additional
formulas are given for computational purposes. For
example:
- If X = interval
level, Y = interval level:
- If X = dichotomous, Y
= interval:
Note: this is the same
measure as an independent groups t test: we have 2
groups, each measured on Y. Where as t is a test of
the significance of the X and Y relationship, the
point biserial is a measure of the magnitude of this
relationship.
- If X and Y are both
dichotomous:
Note: This is essentially a
chi square contingency table. Here chi square would be
the test of signficance while phi is the measure of
magnitude. A similar measure exists for situations where
the number of rows and columns are greater than 2;
however, this related measure is not a PPMC.
- If X and Y are both ordinal:
Kendall's Tau is
another measure of magnitude which can be used when
both X and Y are ordinal. Kendall's Tau is not a
PPMC, but is beneficial in cases where there are many
tied ranks.
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