SECTION 1.5 A REVIEW OF STATISTICAL INFERENCE 31

error. How can the power of an experimental methodology be increased
for a given type | error rate? Two approaches were suggested in Section
1.3. One approach is to increase the size of the sample. A second approach
is to use ar experimental design that provides for a more precise estimate
of treatment effects and a smaller error variance.

If information concerning the true parameter is available, the
probability of committing a type II error can be determined. Generally,
however, the value of the parameter is unknown. In practice, an experi-
menter can specify various possible values of the parameter of interest to
him and then compute the probability of committing a type II error and
1 — B, given that the specified value of ju is true. Let us assume that the
obtained sample statistic is egual to 102.5 and that an experimenter is
interested in determining the probability of correctly rejecting H, if the
population mean is really egual to 103. The probabilities B and 1 — B
can be determined from

X-u 1005-1030

CENI:

According to the normal distribution table in Appendix D.3, the prob-
abilities B and 1 — are .37 and .63, respectively. The location of the
regions corresponding to B and | — B are shown in Figure 1.5-3. In this
example the probability of making a correct decision if ja — 103 is only .63,
whereas the corresponding probability if ja < 100 is .95. The probabilities
associated with the possible outcomes of our decision rule are summarized
in Table 1.5-2.

—-.33.

correct .
TABLE 1.5-2 Probabilities Associated with the

to 103, sea
Decision Process
r prob-
leciding H True Situation
H,. The
1.5-1. au < 100 a < 103
type II error
pu < 10 1-as 95 B < .37
Decision
type | error
a — 103 a < 05 1—-B< 63
SELECTION OF A LEVEL FOR a
In the preceding hypothetical example, the probability of a type I
. error (4) is much lower than the corresponding type II error (B). Experi-
esign and menters in the behavioral sciences freguently set the type I error rate at

ven type 1

05 or .O1. This convention is based primarily on the notion that a type |