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Chapter 6

PROBABILITY AND HYPOTHESIS TESTING
Understanding Statistics for International Social
Work and Other Behavioral Sciences
Serge Lee, Maria C Silveira Nunes Dinis, Lois Lowe and
Kelly Anders (2015). Oxford University Press
HYPOTHESIS TESTING
2
Hypothesis is a statement of an educational hunch or speculation about a
presumed relationship in the real world
Two types of theses:
• Research Hypothesis. Such hypothesis predicts how changes in one variable (independent)
are proposed to cause or explain changes in another variable (dependent). For example, the
average healthcare needs for people without health insurance are twice as much as those
who have health insurance.
• Null Hypothesis. Such hypothesis states that despite what the sample data suggests, after
taking into account sampling errors or chance fluctuations, no real relationship or difference
exits between the hypothesized statements. For example, children whose parents are
supportive of them at school have the same level of self-esteem scores as children whose
parents are not supportive.
DIRECTION OF THE HYPOTHESIS
3
When testing a hypothesis, one may use a
directional or non-directional hypothesis
Directional (one-tailed) hypothesis is used
to test hypotheses that researchers are
certain of or able to predict the direction
that the relationship will fall on the normal
curve
Non-directional (two-tailed) hypothesis is
used to test hypotheses where researchers
believe that significant difference do exist
but are unsure or unable to predict the
direction of the relationship.
CONSTRUCTING THE CONFIDENCE INTERVAL
4
Chance is refers to as
sampling error that
can affect variation
between or among
variables in sample
statistics
Probability is a
mathematical
equation that shows
the proportion or
fraction of times that
a particular outcome
will occur
Probability of an event =
x 100%
Confidence interval,
allows the researchers to
construct an interval or
range of scores around a
point estimate, and
allows the researchers to
state a level of
confidence in how likely
it is that the interval
contains the population
parameters being
estimated
FOUR POSSIBLE OUTCOMES ASSOCIATED
WITH HYPOTHESIS TESTING
5
Determine whether to accept or reject the null hypothesis
Decision regarding the
null hypothesis ()
The truth regarding the research
hypothesis (
is True
is False
Reject
Correct decision
Type I error
Fail to reject
Type II error
Correct decision
Lee. Dinis, Lowe, Anders (2015). Understanding statistics for international social work and other behavioral sciences. Oxford University Press
ALTERNATIVE EXPLANATIONS
6
Use the following possible explanations to
support findings when the research hypothesis
cannot be explained
Rival hypothesis.
Other variables
that may cause a
relationship to
occur
Design flaws.
Design flaws
occur when the
researchers are not
careful with the
measuring
instruments and
sampling bias
Sampling error.
Sampling error
usually occurs due
to unequal sample
size, small sample,
and changes of
data collection
procedures