
 REVIEW
OF HYPOTHESIS TESTING
Two types of
hypotheses
 Research
hypothesis: a succinct statement of a relationship
that exists between two clearly specified
variables.
 Nondirectional
hypothesis:
 (Example: A
person's activity within the community is related
to his educational background.)
 Directional
hypothesis:
 (Example: The
greater the education, the greater the community
activity.)
 Research hypotheses
are supposed to be forcefully stated to permit their
falsification or disproof, if possible.
 Social scientists
are interested in the construction of theory to
explain human behavior on the basis of causal
laws.
 But because
correlation does not mean causation, the
observance of correlations between variables as
hypothesized never proves a
theory.
 Rather, theories
becomes accepted as true as they consistently
resist attempts to disprove
them.
 The lack of a
hypothesized correlation means that causation does
not exist, at least under the conditions of the
theory as specified.
 Thus, science
advances really through attempts at disproving
hypotheses rather than proving them, which
requires that hypotheses be stated clearly in an
attempt to facilitate attempts at disproof.
 Null hypothesis:
To facilitate the disproof of a research hypothesis,
researchers adopt the ploy of constructing a null
hypothesis, which is customarily a statement that no
relationship exists between the variables that are linked
together in the research hypothesis.
 A null hypothesis is
usually constructed as the hypothesis to be tested by
the data because the researcher usually cannot be
specific enough about the strength of the relationship
expected by the research hypothesis.
 The rejection of the
null hypothesis of no relationship, therefore, would
lend support of the research hypothesis by
implication.
Steps in testing hypotheses
 Making
assumptions
 about the population
from which the sample was drawn
 about the sampling
procedure used.
 Obtaining the
sampling distribution of the statistics
 Many statistics, like
the mean, have known sampling
distributions.
 Knowing the sampling
distribution, one can calculate the standard error of
the statistic for samples of varying
sizes.
 Knowing the standard
error means knowing the likely margin of error that
one might encounter purely due to sampling error if
the null hypothesis of no relationship were in fact
true.
 Considerations of the
sampling distributions of the statistic are
incorporated into formulas given to test the
significance of a statistic.
 Selecting a
significance level and critical
region
 According to
probability theory one might observe very rare events
by the operation of purely chance factors  e.g., we
might observe high correlations between two variables
for cases selected at random from some population when
in fact there was no correlation between the variables
in the population from which the cases were
drawn.
 Therefore, we must
specify in advance some probability level such that
the observance of so rare an event  so deviant a
correlation from the expected distribution of
correlations given a true absence of a relationship
between the variables  would be interpreted as
evidence that the assumption of no relationship (the
null hypothesis) must be rejected.
 This specified
probability level is known as the level of
significance and is referred to as the
alpha value.
 It is commonly set
to .05 or .01 in social research, which is largely
a matter of convention.
 A correlation
coefficient or any observed test statistic that is
"significant" at the .05 or .01 levels is one that
is judged to be unlikely to occur simply on the
basis of chance or sampling variation if there were
no relationship within the population (or whatever
the null hypothesis might assert).
 The value of alpha
(e.g., .05 or .01), which expresses the level of
significance, merely states how unlikely an
event must be (i.e., how deviant a correlation must
be) before observing the event will result in
rejecting the null hypothesis.
 This selected
alpha value is associated with a critical
value which marks the region of
rejection) in the sampling distribution; if the
observed test statistic falls within the region of
rejection, the null hypothesis is rejected and it
is presumed that there is some relationship between
the variables.
 When one rejects
the null hypothesis on the basis of a sample value,
one is running the risk of rejecting the null
hypothesis when it is true  which means
claiming that there really is a relationship
between the variables when there is
not.
 This type of
error is called a Type I error, and it is
equal to alpha.
 In general,
reducing the size of the alpha value reduces the
probability of making a Type I error; but as one
reduces alpha, one runs the risk of making a
Type II error.
 A Type II error
means accepting the null hypothesis when it
is false, which in turn means claiming that
there is no relationship between the variables
(as specified by your null hypothesis) when in
fact there is a relationship.
 The
probability of making a Type II error is
equal to beta.
 In general,
the probabilities of making alpha and beta
errors are inversely related;
minimizing the risk of a Type I error,
increases the risk of a Type II
error.
 But the
probability of a Type II error is not just
the complement of a Type I error, and
calculating the value of beta varies
with the statistic, the sample
size, and the
hypothesis.
 In general,
however, the beta error is related to sample
size; the larger the sample, the less the
risk of a Type II
error.
Computing the test statistic: enter the table with
the appropriate distribution
Test Statistic

Distribution

zscore

normal

tvalue

t

Fvalue

F

Making the
decision
 Compare the value of
the test statistic with that expected under the null
hypothesis, usually 0.
 Allow for the
standard error of the statistic by applying the
correct test.
 Enter the appropriate
table to determine the "deviancy" of the observed
statistic when tested against the null hypothesis and
observe if the value falls within the critical region,
allowing for onetailed or twotailed
tests.
