Russel-Research-Method-in-Anthropology

Univariate Analysis 585
would be normal and form a bell curve like the one at the top of figure 19.4
and in figure 7.1.
The unlikely means (the very large ones and the very small ones) show up
in the narrow area under the tails of the curve, while the likely means (the
ones closer to the true mean of the population) show up in the fat, middle part.
In research, the question you want to answer is whether the means of variables
from one, particular sample (the one you’ve got) probably represent the tails
or the middle part of the curve.
Hypothesis tests are two tailed when you are interested only in whether the
magnitude of some statistic is significant (i.e., whether you would have
expected that magnitude by chance). When the direction of a statistic is not
important, then a two-tailed test is called for.
As we’ll see in chapter 20, however, when you predict that one of two
means will be higher than the other (like predicting that the mean of the final
exam will be higher than the mean of the midterm exam in a class) you would
use a one-tailed test. After all, you’d be asking only whether the mean was
likely to fall in one tail of the normal distribution. Look at appendix C carefully.
Scores significant at the .10 level for a two-tailed test are significant at
the .05 level for a one-tailed test.
4. Finally, we determine the alpha level, written , which is the level of significance
for the hypothesis test. Typically, alpha is set at the .05 level or at the .01
level of significance. What this means is that if a mean or a proportion from a
sample is likely to occur more than alpha—say, more than 5% of the time—then
we fail to reject the null hypothesis.
And conversely: If the mean or a proportion of a sample is likely to occur
by chance less than alpha, then we reject the null hypothesis. Alpha defines the
critical region of a sampling distribution—that is, the fraction of the sampling
distribution small enough to reject the null hypothesis.
In neither case do we prove the research hypothesis, H 1 . We either reject or
fail to reject the null hypothesis. Failing to reject the null hypothesis is the
best we can do, since, in a probabilistic science, we can’t ever really prove any
research hypothesis beyond any possibility of being wrong.
On Being Significant
By custom—and only by custom—researchers generally accept as statistically
significant any outcome that is not likely to occur by chance more than
five times in a hundred tries. This p-value, or probability value, is called the
.05 level of significance. Ap-value of .01 is usually considered very significant,
and .001 is often labeled highly significant.