The following extract is taken with permission from the third edition of
the Wiley text by Good and Hardin, Common Errors in Statistics (and How
to Avoid Them):
Null Hypothesis
"A major research failing seems to be the exploration of uninteresting
or even trivial questions...In the 347 sampled articles in Ecology
containing null hypotheses tests, we found few examples of null
hypotheses that seemed biologically plausible." Anderson, Burnham, and
Thompson [2000].
“We do not perform an experiment to find out if two varieties of wheat
or two drugs are equal. We know in advance, without spending a dollar
on an experiment, that they are not equal.” Deming (1975).
Test only relevant null hypotheses
The "null hypothesis" has taken on an almost mythic role in contemporary
statistics. Obsession with the "null" has been allowed to shape the
direction of our research. We've let the tool use us instead of our
using the tool.
While a null hypothesis can facilitate statistical inquiry—an exact
permutation test (as discussed in Chapters 5 and 7) is impossible
without it—it is never mandated. In any event, virtually any
quantifiable hypothesis can be converted into null form. There is no
excuse and no need to be content with a meaningless null.
For example, suppose we want to test that the effect of a given
treatment will be to decrease the need for bed rest by at least three
days. Previous trials have convinced us that the treatment will reduce
the need for bed rest to some degree, so merely testing that the
treatment has a positive effect would yield no new information.
Instead, we would subtract three from each observation and then test the
"null hypothesis" that the mean value is zero.
We often will want to test that an effect is inconsequential, not zero
but close to it, smaller than d, say, where d is the smallest
biological, medical, physical or socially relevant effect in our area of
research. Again, we would subtract d from each observation before
proceeding to test a null hypothesis.
The quote from Deming above is not quite correct as often we will wish
to demonstrate that two drugs or two methods yield equivalent results.
As shown in Chapter 5, we test for equivalence using confidence
intervals; a “null hypothesis” is not involved
To test that "80% of redheads are passionate," we have two choices
depending on how "passion" is measured. If "passion" is an all or none
phenomena, then we can forget about trying to formulate a null
hypothesis and instead test the binomial hypothesis that the probability
p that a redhead is passionate is 80%. If "passion" can be measured on
a seven-point scale and we define "passionate" as "passion" greater than
or equal to 5, then our hypothesis becomes "the 20th percentile of
redhead passion exceeds 5." As in the first example above, we could
convert this to a "null hypothesis" by subtracting five from each
observation. But the effort is unnecessary as this problem, too,
reduces to a test of a binomial parameter.
You may leave the list at any time by sending the command
SIGNOFF allstat
to [log in to unmask], leaving the subject line blank.
|