Russel-Research-Method-in-Anthropology

Univariate Analysis 591
of Shipibo Indian children in Peru. They weighed and measured 149 infants,
from newborns to 36 months in age.
By converting all measurements for height and weight to z-scores, they
were able to compare their measurements of the Shipibo babies against standards
set by the World Health Organization (Frisancho 1990) for healthy
babies. The result: By the time Shipibo children are 12 months old, 77% of
boys and 42% of girls have z-scores of 2 or more on length-for-age. In other
words, by a year old, Shipibo babies are more than two standard deviations
under the mean for babies who, by this measure, are healthy.
By contrast, only around 10% of Shipibo babies (both sexes) have z-scores
of 2 or worse on weight-for-length. By a year, then, most Shipibo babies
are clinically stunted but they are not clinically wasted. This does not mean
that Shipibo babies are small but healthy. Infant mortality is as high as 50%
in some villages, and the z-scores on all three measures are similar to scores
found in many developing countries where children suffer from malnutrition.
z-scores do have one disadvantage: They can be downright unintuitive.
Imagine trying to explain to people who have no background in statistics why
you are proud of having scored a 1.96 on the SAT. Getting a z-score of 1.96
means that you scored almost two standard deviations above the average and
that only 2.5% of all the people who took the test scored higher than you did.
If you got a z-score of .50 on the SAT, that would mean that about a third
of all test takers scored lower than you did. That’s not too bad, but try explaining
why you’re not upset about getting a minus score on any test.
This is why T-scores (with a capital T—not to be confused with Student’s t)
were invented. The mean of a set of z-scores is always 0 and its standard deviation
is always 1. T-scores are linear transformations of z-scores. For the SAT
and GRE, the mean is set at 500 and the standard deviation is set at 100. A
score of 400 on these tests, then, is one standard deviation below the mean; a
score of 740 is 2.4 standard deviations above the mean (Friedenberg 1995:85).
The Univariate Chi-Square Test
Finally, chi-square (often written 2 ) is an important part of univariate analysis.
It is a test of whether the distribution of a series of counts is likely to be
a chance event. The formula for 2 is:
2 (OE)2
Formula 19.10
E
where O represents the observed number of cases and E represents the number
of cases you’d expect, ceteris paribus, or ‘‘all other things being equal.’’