Distinction between
NONDIRECTIONAL and DIRECTIONAL research
hypotheses
 Nondirectional
hypotheses
 Only state that one
group differs from another on some characteristic,
i.e., it does NOT specify the DIRECTION of the
difference
 Example:
H_{0}  Northwestern students differ from the
college population in ideological
attitudes
 Directional
hypotheses
 Specifies the nature
of the difference, i.e., that one group is higher, or
lower, than another group on some
attribute
 Example:
 NU students are
more conservative than other students =
H_{1}
 NU students are
more liberal than other students =
H_{2}

DIRECTIONS and TAILS in hypotheses and statistical
tests
Nondirectional
hypotheses use twotailed tests
 Any evidence of
difference between NU students and the population
supports a nondirectional research
hypothesis.
 The appropriate test
is against the null hypothesis, H_{0}:
= 0
 Values different from
0, in either direction, are used in computing the test
statistic, a zvalue (or t, depending on sample
size)
 Either large
positive zscores or large negative
zscores can lead to the rejection of the null
hypothesis
 Thus the regions of
rejection must lie in both tails of the normal
distribution
 Assuming an alpha level
of .05:
 the rejection region
to the right is marked by the critical value of
+1.96 and contains .025 of the cases
 that to the left is
at 1.96 and also contains .025 of cases
 Hence, a test of a
nondirectional hypothesis is a twotailed
test
Directional
hypotheses use onetailed tests
 Directional
research hypothesis: NU students are more
conservative (higher on the scale) than other students
H_{1}:
> 0
 Any finding that shows
NU students to be more liberal (lower on the scale) would
directly contradict the research hypothesis
 The proper test is
against this "null" hypothesis
H_{0}:
< (or =) 0
 Now, only large
positive zscores can reject this null
hypothesis.
 Assuming an alpha
level of .05:
 the region of
rejection is fixed entirely in the right hand
tail of the distribution
 the righthand
tail alone must now contain .05 of the
cases
 the critical
value now becomes a zscore of +1.65
 .4505 cases lie
between 0 and 1.65
 .0495 (close
enough to .05) lie to the right of
1.65
 The size of the
region of rejection remains the same (.05), but it
lies only in one tail of the distribution, so it is
marked by a smaller critical value: 1.65 <
1.96.
 Hence, a
onetailed test offers a better chance to reject
your null hypothesis
Errors in making statistical decisions
 Type I error: The
probability of rejecting a true null hypothesis is
equal to the alpha level.
 Type II error:
The probability of accepting the null hypothesis when it
is false (the beta value) is not easily calculated
 As stated in the
syllabus:
Type I
and Type II errors . . . are hard to keep
straight, and even most researchers have to think
hard before explaining the difference. An analogy
with diagnosing anthrax may help.
 Type I:
A doctor rejects the hypothesis that the patient
has anthrax and fails to prescribe cipro. The
patient did have it and died.
 Type II:
A doctor accepts the hypothesis that the
patient has anthrax and prescribes cipro. The
patient didn't have it, cipro destroyed
the patients' immune system, and the patient
died of influenza.

Comments on directional hypotheses
 It requires more theory
to predict direction as well as
difference
 Because the predictions
are more precise, you can count more outcomes against
your hypothesis: i.e., those in the wrong
direction
 This permits using
onetailed tests, which do not need as much difference
between observed and predicted values to yield
significance
 Moral: formulate
directional hypotheses and use onetailed tests when
possible, e.g., in your research
papers.
