Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 635
150
150
INFMORT
100
50
INFMORT
100
50
0
0 10000 20000 30000 40000
a. PCGDP
b.
0
4 5 6 7 8 9 10 11
LOGPCGDP
Infant mortality by per capita gross domestic
product for 50 countries in table 19.8.
Figure 20.7. Transforming variables.
Infant mortality and the log of per capita
gross domestic product for 50 countries in
table 19.8.
by a factor of five to cut their infant mortality rate in half. At $5,000 per year,
countries only have to double PCGDP to halve infant mortality rate. And at
$10,000 per year, it only takes a 50% rise in PCGDP to halve the infant mortality
rate again.
If a scatterplot looks anything like figure 20.7a, consider transforming the
data into their logarithms. If a scatterplot looks like the shapes in figures 20.5
or 20.6, then consider using eta-squared, a statistic for nonlinear regression.
Calculating Eta-Squared
Eta-squared, written 2 or eta 2 , is a PRE measure that tells you how much
better you could do if you predicted the separate means for chunks of your
data than if you predicted the mean for all your data. Figure 20.8 graphs the
hypothetical data in table 20.19. These data show, for a sample of 20 people,
ages 12–89, their ‘‘number of close friends and acquaintances.’’
The dots in figure 20.8 are the data points from table 20.19. Respondent
10, for example, is 45 years of age and was found to have approximately 55
friends and acquaintances. The horizontal dashed line in figure 20.8 marked y
is the global average for these data, 41.15.
Clearly: (1) The global average is not of much use in predicting the dependent
variable; (2) Knowing a person’s age is helpful in predicting the size of