SECTION 1.5 A REVIEW OF STATISTICAL INFERENCE 25

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leads to a prediction, or anticipated value, and to a hypothetical sampling
distribution of anticipated values for a sample statistic. If the sample
statistic eguals the anticipated value, or falls in a region of the sampling
distribution designated as a probable anticipated value, a decision is made
to accept the null hypothesis. On the other hand, if the sample statistic
deviates appreciably from the anticipated value, either a rare and improbable
event has occurred or the null hypothesis has led to a poor prediction and
should be rejected.

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poth-

HYPOTHESIS TESTING
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ns; for Hypothesis testing appears to be a straightforward objective pro-
cedure until an attempt is made to define such phrases as "probable
anticipated value," "deviates appreciably," and "poor prediction." On what
basis does one decide which anticipated values are probable, or when the
sample statistic deviates appreciably from the anticipated value, or when a
null hypothesis leads to a poor prediction? The answer to these guestions
in the behavioral sciences is that the experimenter falls back on a set of
conventions. A branch of mathematics known as decision theory deals
with the problem of choosing optimum decision rules. Although hypoth-
esis-testing procedures in the behavioral sciences use many notions
from decision theory, the application is incomplete and research is fre-
guently conducted according to rules that are less than optimum for the
experimenter's purposes.

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STEPS FOLLOWED IN TESTING A HYPOTHESIS

What conventions are currently used in testing a hypothesis?
These conventions can be summarized in four steps.

Step 1: State a null hypothesis 4, and an alternative hypothesis H,.

Step 2: Decide on an appropriate sample statistic and test statistic. The
selection of a test statistic is based on (l) H,, (2) the chosen sample
statistic, and (3) tenable assumptions concerning the population
distributions. Assumptions underlying the sampling distributions of
gih and F test statistics are discussed in Section 2.1.

sciences

Step 3: Decide on a level of significance x and a sample size N. a and N,
together with the sampling distribution of the test statistic under the
null hypothesis, determine the region for rejecting H.
The location and size of the region for rejection of the null hypothesis
are determined by H, and a, respectively. An experimenter attempts to
select a level of significance so that the region of rejection contains
values of the test statistic that have a low probability of occurrence if
H, is true but a high probability if H, is true.

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Step 4: Obtain the sample statistic and compute the test statistic. If the value
of the test statistic falls in the region of rejection, H, is rejected in
favor of H,. If the test statistic falls outside the region of rejection, the
experimenter may either accept H, or suspend making a decision

n the light concerning it.

hypothesis