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INTRODUCTION TO BASIC CONCEPTS IN EXPERIMENTAL DESIGN

exhaustive hypotheses is to be rejected and which one is to be accepted at
some specified risk of making an incorrect decision (Clark, 1963).

A statistical hypothesis can be either exact or inexact. The hypoth-
esis that the mean (4) of population j is egual to 40

(1) H,: u; < 40
is an exact hypothesis. The hypothesis
(2) Ho: u; s 4

is an example of an inexact hypothesis. The alternative (H,) to the exaci
null hypothesis above can take any one of several different forms; for
example,

H,: ua; < 43 (exact alternative hypothesis)
H, : a; £ 40 (inexact two-tailed alternative hypothesis).
The alternative to the inexact null hypothesis above can be written
H,:u,;> 4.
If a comparison of the central tendency of two populations j and j' is of
interest, the null and alternative hypotheses can take any of the following
forms:
Ho: K; — MU; — 0
H,:u;- an b0
Or

H,:uj- Hj SO

Or

H,: u; — uy <0.

It should be noted that hypothesis testing in the behavioral sciences
usually involves either two inexact hypotheses or one exact and one in-
exact hypothesis. The distinction between exact and inexact hypotheses is
unimportant from a practical standpoint because the same general test
procedures are followed in each case. Although we may speak of testing a
single hypothesis, in practice we behave as though we were deciding which
one of two mutualiy exclusive and exhaustive hypotheses is supported by

our data. The procedure by which we make this decision 1s called a statistical
test.

STATISTICAL TEST

A statistical test is the comparison of two hypotheses in the light
of sample data according to a set of decisior rules. The null hypothesis