You are testing to see if a new drug, which is intended to lower blood
pressure, has as a side effect induction of cancer. Your subjects are rats,
and you know the base rate of cancer in this population of untreated rats.
The null hypothesis is that the new drug does not increase cancer rate, that
is, in treated rats the rate is less than or equal to the base rate, that is,
the drug is safe. The alternative hypothesis is that the drug is unsafe, does
increase cancer rate.
Now you test the effectiveness of the drug. Your null hypothesis is that
treatment produces zero or less reduction in blood pressure, it is not
effective. The alternative is that is does reduce blood pressure, it is
effective.
For each of these scenarios I ask my students to consider which is the
more serious error -- "Type I" or "Type II." Most agree that a Type II error
(drug is actually unsafe, we conclude it is safe) is more serious than a
Type I error (drug is safe, we conclude it is not), in the first scenario,
and most agree that in the second a Type I error (drug is not effective, but
we conclude it is effective) is more serious than a Type II error (drug is
effective, we conclude it is not)
As noted in an earlier post, the null hypothesis is the one which
specifies a value of the tested parameter.
From this point I try to convince my students that one should set the
"alpha-criterion" (for rejecting the null) by considering the relative
seriousness of Type I and Type II errors for the particular circumstances
in which the test is being used. This leads into discussion of Beta, Power,
choosing sample sizes sufficiently large so that meaningful effects, if they
exist, are nearly certain to be detected (and if they are not detected, one
may be able to conclude they likely do not exist). One can also discuss how
different persons might have different perspectives on the relative
seriousness of Type I and Type II errors in a given situation -- a stockholder
of the drug company might differ from a potential consumer for the scenarios
above. Some students will ask very relevant questions, such as "Are there
other drugs that are effective for this condition?" or "Might the benefit of
effective treatment outweigh some elevated risk of developing cancer?"
Of course, one might also suggest that there may be inferential techinques
more useful than traditional hypothesis testing in circumstances like this,
but when preparing students to enter a discipline dominated by traditional
statistical techniques, one might better just bite e's tongue, at least
during the first semester course, eh?
Karl L. Wuensch, Dept. of Psychology, East Carolina Univ.
Greenville, NC 27858-4353, phone 919-328-6800, fax 919-328-6283
Bitnet Address: PSWUENSC@ECUVM1
Internet Address: PSWUENSC@ECUVM.CIS.ECU.EDU