Introduction to Inferential Statistics and Hypothesis Testing
Review
•
Definition of “unlikely”
o
At minimum .05 or 5%
•
Sample is a stastic and population is a parameter
o
Discrepancy between statistic and parameter is a sampling error
Examples to consider:
1. Sometimes correlations are rather small, such as physical attractiveness and selfesteem (r = .15). That’s what was
found in the sample. Is this just kind of a random thing we found in this sample or does that relationship exist in the
population?
2. Another common research situation involves comparing groups. Imagine that researchers test a new method for
teaching children to read. They randomly assign half of a sample to receive the new teaching method. The other half
does not; they are the control group. All of the children take a reading test at the end of the study, and the mean for
one group is 5 points lower than the mean for the other group. Is this a real difference? Does this generalize to the
population so that we can make a statement about the effect of teaching method on reading?
There are always two possible interpretations of the sample result:
1.
The result is due to chance/error.
2.
The result is not due to chance. The sample accurately reflects what is really happening in the population.
Inferential statistics allows us to evaluate these two possibilities. In order to do this, we must use hypothesis testing and
probability.
Hypothesis testing
Hypothesis testing
: Method of using sample data to evaluate a claim about a
population parameter
; a method for
making rational decisions about the reality of our sample results.
When dealing with hypothesis testing
– there are two hypothesis – very discrete and mututal exclusive way
1. Two types of hypotheses:
a. Null hypothesis:
There is no effect, no relationship, no difference, nothing real in the population
H
0
: IV does not affect DV.
OR
H
0
:
parameter = 0
b. Alternative hypothesis:
There is an effect, a relationship, a difference, something is happening.
H
1
:
IV affects DV.
OR
H
1
: parameter
≠
0
[A side note about directional vs. nondirectional hypotheses:
•
directional hypothesis specficy that the direction of the effect (it will be higher, greater, etc,)
•
nondirectional hypothesis does not specify (could be higher or lower)
•
we will focus on the former
c. Examples of null and alternative hypotheses
1) Relationship between physical attractiveness and selfesteem
H
0
: There is no relationship between physical attractiveness and selfesteem. (WORDS VERSION)
H
0
: p = 0 (SYMBOLS VERSION)
H
1
: There is a relationship between physical attractiveness and selfesteem.
H
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 Fall '08
 Burns

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