Russel-Research-Method-in-Anthropology

Multivariate Analysis 659
ideas about some antecedent or intervening variables are plausible by showing
what could be going on—but they don’t tell you how things work or how much
those antecedent or intervening variables are contributing to a correlation you
want to understand. For that, we need something a bit more . . . well, elaborate.
Partial correlation is a direct way to control for the effects of a third (or fourth
orfifth...)variable on a relationship between two variables.
Here’s an interesting case. Across the 50 states in the United States, there
is a stunning correlation (r .778) between the percentage of live births to
teenage mothers (15–19 years of age) and the number of motor vehicle deaths
per hundred million miles driven. States that have a high rate of road carnage
have a high rate of births to teenagers, and vice versa.
This one’s a real puzzle. Obviously, there’s no direct relation between these
two variables. There’s no way that the volume of highway slaughter causes the
number of teenage mothers (or vice versa), so we look for something that
might cause both of them.
I have a hunch that these two variables are correlated because they are both
the consequence of the fact that certain regions of the country are poorer than
others. I know from my own experience, and from having read a lot of
research reports, that the western and southern states are poorer, overall, than
are the industrial and farming states of the Northeast and the Midwest. My
hunch is that poorer states will have fewer miles of paved road per million
people, poorer roads overall, and older vehicles. All this might lead to more
deaths per miles driven.
Table 21.14 shows the zero-order correlation among three variables:
motor vehicle deaths per hundred million miles driven (it’s labeled MVD in
TABLE 21.14
Correlation Matrix for Three Variables
Variable 1 Variable 2 Variable 3
MVD TEENBIRTH INCOME
MVD 1.00
TEENBIRTH .778 1.00
INCOME .662 .700 1.00
SOURCE: MVD for 1995, Table 1018, Statistical Abstract of the United States (1997). TEENBIRTH for 1996,
Table 98, Statistical Abstract of the United States (1997). INCOME for 1996, Table 706, Statistical Abstract of
the United States (1997).
table 21.14); the percentage of live births to young women 15–19 years of age
(TEENBIRTH); and average personal income (INCOME). Zero-order correlations
do not take into account the influence of other variables.
We can use the formula for partial correlation to test directly what effect, if