Russel-Research-Method-in-Anthropology

588 Chapter 19
t (19.4925.51)/6.58 0.91
We can test whether the value of t is statistically significant by referring to
the t-table in appendix C. To use appendix C, we need to know: (1) how many
degrees of freedom we have and (2) whether we want a one- or a two-tailed
test.
To understand the concept of degrees of freedom, suppose I give you a jar
filled with thousands of beans numbered from 1 to 9 and ask you to pick two
that sum to 10. If you pick a 4 on the first draw, then you must pick a 6 on the
next; if you pick a 5 on the first draw, then you must pick another 5; and so
on. This is an example of one degree of freedom, because after the first draw
you have no degrees of freedom left.
Suppose, instead, that I ask you to pick four beans that sum to 25. In this
example, you have three degrees of freedom. No matter what you pick on the
first draw, there are lots of combinations you can pick on the next three draws
and still have the beans sum to 25. But if you pick a 6, a 9, and a 7 on the first
three draws, then you must pick a 3 on the last draw. You’ve run out of degrees
of freedom.
For a one-sample, or univariate t-test, the degrees of freedom, or df, is simply
n 1. For the sample of 10 representing FEMILLIT there are 10 1
9 degrees of freedom.
Testing the Value of t
We’ll use a two-tailed test for the problem here because we are only interested
in whether our sample mean, 19.49, is significantly different from, the
population mean of 25.51. Thus, the null hypothesis is that 19.49% could be
found just by chance if we drew this sample of 10 countries from a population
of countries where the mean is 25.51%.
Looking at the values in appendix C, we see that any t-value above 2.262 is
statistically significant at the .05 level with 9 degrees of freedom for a twotailed
test. With a t-value of .91 (we only look at the absolute value and
ignore the minus sign), we can not reject the null hypothesis. The true mean
percentage of female illiteracy rates across the 50 countries of the world is
statistically indistinguishable from 19.49%.
Testing the Mean of Large Samples
Another way to see this is to apply what we learned about the normal distribution
in chapter 7. We know that in any normal distribution for a large popu-