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SECTION 1.5 A REVIEW OF STATISTICAL INFERENCE

SEAN a Z ——<—

"All rats run under condition X." Such hypotheses can be evaluated by
inductive inference only and must be reducible to direct statements.
The chain of events reguired in testing an indirect statement is shown

in Figure-l.5-1.

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Figure 1.5-1
deductive and inductive inferences.

If, in Figure 1.5-1, the term scientific hypothesis is substituted for
indirect statement and statistical hypothesis for direct statement, the
analogy with hypothesis testing is readily apparent. The experimenter
has the task of translating his research hypotheses into a dichotomous
set of mutually exclusive statistical hypotheses. It should be noted that the
chain of deductive reasoning from a guestion concerning nature to a
research hypothesis to a statistical hypothesis and the reverse process of
inductive reasoning from the statistical hypothesis to the guestion is an
exercise in logic rather than statistical inference. If an error occurs in the
chain, the statistical hypotheses subjected to test may have no bearing on
the original guestion, or incorrect inferences concerning the guestion may
be made. Grant (1962), Binder (1963), and Edwards (1965) have examined
in detail the relation between scientific and statistical hypotheses.

KINDS OF STATISTICAL HYPOTHESES

A null hypothesis (H,) is the statistical hypothesis that is subjected
to a test. The notion that the null hypothesis refers to a parameter value of
zero is a simplification; the hypothesis can specify the parameter as having
any value, including zero. Less confusion will result if the null hypothesis
is considered as the hypothesis that is tested. The hypothesis that remains
tenable if the null hypothesis is rejected is called the alternative hypothesis
(H,). Hypothesis testing can be viewed as a procedure whereby an experi-
menter decides which one of a dichotomous set of mutually exclusive and

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