Russel-Research-Method-in-Anthropology

Univariate Analysis 587
rejecting H 0 when we should do exactly that. In this case, the result is that you
place people at greater risk of food-borne disease.
In a probabilistic science, we are always in danger of making one or the
other of these errors. Do we try to avoid one kind more than the other? It
depends on what’s at stake. A Type I error at the .01 level for an HIV test
means that one person out of a hundred is declared HIV-free when they are
really HIV-positive. How big a sample do you need to get that error level
down to one out of a thousand? This is the kind of question answered by
power analysis, which we’ll look at in chapter 20.
So, What about the Mean of FEMILLIT?
As you know from chapter 7, statistics (like the mean) vary from sample to
sample and how much they vary depends on: (1) the size of the sample and
(2) the amount of actual variation in the population from which you take your
sample. The average amount of error we make in estimating a parameter from
sample statistics is called the standard error, or SE, of the statistic. The standard
error of the mean, SEM, is the standard deviation, sd, divided by the
square root of the sample size, n:
SEM sd
n
Formula 19.7
We can calculate the SEM for the sample of 10 countries on the variable FEM-
ILLIT. From table 19.10, we know that x 19.49% and sd 20.81 so:
SEM 20.81
10 6.58
Now, knowing the SEM, we can ask whether the mean of the sample of 10
cases in table 19.7 (19.49%) can be distinguished statistically from the mean
of the population of countries in table 19.8.
Since this is a small sample, we can test this using Student’s t distribution,
which I introduced in chapter 7 (see figure 7.7). We have data on the percentage
of adult female illiteracy for 45 countries in table 19.8, and the mean for
those data is 25.51%. The formula for calculating t, when the parameter, , is
known, is:
t x
SEM
So, for the sample of 10 countries on FEMILLIT,
Formula 19.8