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of values.” or “Some measurable characteristic takes different values in dif-
ferent populations, the difference(s) taking a specific pattern or a specific
set of values.”
Examples of well-formed statistical hypotheses include the following:
•
“For males over 40 suffering from chronic hypertension, a 100 mg
daily dose of this new drug lowers diastolic blood pressure an
average of 10 mm Hg.”
•
“For males over 40 suffering from chronic hypertension, a daily
dose of 100 mg of this new drug lowers diastolic blood pressure
an average of 10 mm Hg more than an equivalent dose of
metoprolol.”
•
“Given less than 2 hours per day of sunlight, applying from 1 to
10 lb of 23-2-4 fertilizer per 1000 square feet will have no effect
on the growth of fescues and Bermuda grasses.”
“All redheads are passionate” is not a well-formed statistical hypothe-
sis—not merely because “passionate” is ill-defined, but because the word
“All” indicates that the phenomenon is not statistical in nature.
Similarly, logical assertions of the form “Not all,” “None,” or “Some”
are not statistical in nature. The restatement, “80% of redheads are pas-
sionate,” would remove this latter objection.
The restatements, “Doris J. is passionate,” or “Both Good brothers are
5¢10≤ tall,” also are not statistical in nature because they concern specific
individuals rather than populations (Hagood, 1941).
If we quantify “passionate” to mean “has an orgasm more than 95% of
the time consensual sex is performed,” then the hypothesis “80% of red-
heads are passionate” becomes testable. Note that defining “passionate” to
mean “has an orgasm every time consensual sex is performed” would not
be provable as it is a statement of the “all or none” variety.
Finally, note that until someone succeeds in locating unicorns, the
hypothesis “80% of unicorns are passionate” is
not
testable.
Formulate your hypotheses so they are quantifiable, testable, and statistical
in nature.
How Precise Must a Hypothesis Be?
The chief executive of a drug company may well express a desire to test
whether “our anti-hypertensive drug can beat the competition.” But to
apply statistical methods, a researcher will need precision on the order of
“For males over 40 suffering from chronic hypertension, a daily dose of
100 mg of our new drug will lower diastolic blood pressure an average
of 10 mm Hg more than an equivalent dose of metoprolol.”
The researcher may want to test a preliminary hypothesis on the order
of “For males over 40 suffering from chronic hypertension, there is a daily
