Russel-Research-Method-in-Anthropology

586 Chapter 19
Many researchers use asterisks instead of p-values in their writing to cut
down on number clutter. A single asterisk signifies a p-value of .05, a double
asterisk signifies a value of .01 or less, and a triple asterisk signifies a value
of .001 or less. If you read: ‘‘Men were more likely than women** to report
dissatisfaction with local schoolteacher training,’’ you’ll know that the double
asterisk means that the difference between men and women on this variable
was significant at the .01 level or better.
And remember: Statistical significance is one thing, but substantive significance
is another matter entirely. In exploratory research, you might be satisfied
with a .10 level of significance. In evaluating the side effects of a medical
treatment, you might demand a .001 level—or an even more stringent test
of significance.
Type I and Type II Errors
There is one more piece to the logic of hypothesis testing. The choice of an
alpha level lays us open to making one of two kinds of error—called, conveniently,
Type I error and Type II error.
If we reject the null hypothesis when it’s really true, that’s a Type I error.
If we fail to reject the null hypothesis when it is, in fact, false, that’s a Type
II error.
Suppose we set alpha at .05 and make a Type I error. Our particular sample
produced a mean or a proportion that happened to fall in one of the 2.5% tails
of the distribution (2.5% on either side accounts for 5% of all cases), but 95%
of all cases would have resulted in a mean that let us reject the null hypothesis.
Suppose the government of a small Caribbean island wants to increase tourism.
To do this, somebody suggests implementing a program to teach restaurant
workers to wash their hands after going to the bathroom and before returning
to work. The idea is to lower the incidence of food-borne disease and
instill confidence among potential tourists.
Suppose you do a pilot study and the results show that H 0 is false at the .05
level of significance. The null hypothesis is that the proposed program is useless,
so this would be great news. But suppose H 0 is really true—the program
really is useless—but you reject it. This Type I error sets off a flurry of activity:
The Ministry of Health requires restaurant owners to shell out for the program.
And for what?
The obvious way to guard against this Type I error is to raise the bar and
set at, say, .01. That way, a Type I error would be made once in a hundred
tries, not five times in a hundred. But you see immediately the cost of this little
ploy: It increases dramatically the probability of making a Type II error—not