Hypotheses: The Why of Your Research - Common Errors in Statistics - page 19

A two-sided alternative dictates a two-tailed test; a one-sided alternative
dictates a one-tailed test.
As an example, suppose we decide to do a follow-on study of the cancer
registry to confirm our original finding that men diagnosed as having
tumors live significantly longer than women similarly diagnosed. In this
follow-on study, we have a one-sided alternative. Thus, we would analyze
the results using a one-tailed test rather than the two-tailed test we applied
in the original study.

Determine beforehand whether your alternative hypotheses are ordered or
unordered.

Ordered or Unordered Alternative Hypotheses?
When testing qualities (number of germinating plants, crop weight, etc.)
from k samples of plants taken from soils of different composition, it is
often routine to use the F ratio of the analysis of variance. For contin-
gency tables, many routinely use the chi-square test to determine if the
differences among samples are significant. But the F -ratio and the chi-
square are what are termed omnibus tests, designed to be sensitive to all
possible alternatives. As such, they are not particularly sensitive to ordered
alternatives such “as more fertilizer more growth” or “more aspirin faster
relief of headache.” Tests for such ordered responses at k distinct treat-
ment levels should properly use the Pitman correlation described by Frank,
Trzos, and Good [1978] when the data are measured on a metric scale
(e.g., weight of the crop). Tests for ordered responses in 2 ¥ C contin-
gency tables (e.g., number of germinating plants) should use the trend
test described by Berger, Permutt, and Ivanova [1998]. We revisit this
topic in more detail in the next chapter.

DEDUCTION AND INDUCTION
When we determine a p value as we did in the example above, we apply a
set of algebraic methods and deductive logic to deduce the correct value.
The deductive process is used to determine the appropriate size of resistor
to use in an electric circuit, to determine the date of the next eclipse of
the moon, and to establish the identity of the criminal (perhaps from the
fact the dog did not bark on the night of the crime). Find the formula,
plug in the values, turn the crank, and out pops the result (or it does for
Sherlock Holmes, 4 at least).
When we assert that for a given population a percentage of samples will
have a specific composition, this also is a deduction. But when we make an

4

See “Silver Blaze” by A. Conan-Doyle, Strand Magazine , December 1892.