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3/16/14 More on Inferential
Statistics
Inferential Statistics
•  What is Significant?
•  An inferential statistical test can tell us whether the results of an
experiment can occur frequently or rarely by chance.
•  Inferential statistics with small values occur frequently by chance.
•  Inferential statistics with large values occur rarely by chance.
•  Null Hypothesis
•  A hypothesis that says that all differences between groups are due to
chance (i.e., not the operation of the IV).
•  If a result occurs often by chance, we say that it is not significant and
conclude that our IV did not affect the DV.
•  If the result of our inferential statistical test occurs rarely by chance (i.e., it
is significant), then we conclude that some factor other than chance is
operative.
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t-test
•  t Test
•  The t test is an inferential statistical test used to evaluate the
difference between the means of two groups.
•  Degrees of Freedom
•  The ability of a number in a specified set to assume any
value.
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1 3/16/14 The t Test
•  Interpretation of t value
•  Determine the degrees of freedom (df) involved.
•  Use the degrees of freedom to enter a t table.
•  This table contains t values that occur by chance.
•  Compare your t value to these chance values.
•  To be significant, the calculated t must be equal to or larger than
the one in the table.
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Inc., Upper Saddle River, NJ 07458. All
rights reserved.
One-Tail Versus Two-Tail Tests of
Significance
•  Directional versus Nondirectional Hypotheses
•  A directional hypothesis specifies exactly how (i.e., the direction)
the results will turn out.
•  A nondirectional hypothesis does not specify exactly how the
results will turn out.
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One-Tail Versus Two-Tail Tests of
Significance
•  One-tail t test
•  Evaluates the probability of
only one type of outcome
(based on directional
hypothesis).
•  Two-tail t test
•  Evaluates the probability of
both possible outcomes (based
on nondirectional hypothesis).
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2 3/16/14 The Logic of Significance
Testing
•  Typically our ultimate interest is not in the samples we
have tested in an experiment but in what these samples
tell us about the population from which they were
drawn.
•  In short, we want to generalize, or infer, from our
samples to the larger population.
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The Logic of Significance Testing
A.  Random samples are drawn
from a population.
B.  The administration of the IV
causes the samples to differ
significantly.
C.  The experimenter generalizes
the results of the experiment
to the general population.
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Type I and Type II Errors
•  Type I (alpha) Error – false positive
•  Accepting the experimental hypothesis when the null hypothesis
is true.
•  The experimenter directly controls the probability of making a
Type I error by setting the significance level.
•  You are less likely to make a Type I error with a significance level of .
01 than with a significance level of .05
•  However, the more extreme or critical you make the significance level
to avoid a Type I error, the more likely you are to make a Type II
(beta) error.
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3 3/16/14 Type I and Type II Errors
•  Type II (beta) Error – false negative
•  A Type II error involves rejecting a true experimental hypothesis.
•  Type II errors are not under the direct control of the
experimenter.
•  We can indirectly cut down on Type II errors by implementing
techniques that will cause our groups to differ as much as
possible.
•  For example, the use of a strong IV and larger groups of
participants.
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Type I and Type II Errors
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Example
•  Suppose a researcher comes up with a new drug that
in fact cures AIDS. She assigns some AIDS patients
to receive a placebo and others to receive the new
drug. The null hypothesis is that the drug will have
no effect.
•  In this case, what would be the Type I error?
•  In this case, what would be the Type II error?
•  Which do you think is the more costly error? Why?
4 3/16/14 TYPE I AND TYPE II
ERRORS
•  The probability of
making a Type I error
–  Set by researcher
•  e.g., .01 = 1%
chance of rejecting
null when it is true
•  e.g., .05 = 5%
chance of rejecting
null when it is true
–  Not the probability of
making one or more
Type I errors on
multiple tests of null!
•  The probability of
making a Type II error
–  Not directly controlled
by researcher
–  Reduced by increasing
sample size
MAKING A DECISION
If You…
When the Null
Hypothesis Is Actually…
Then You Have…
Reject the null hypothesis
True (there really are no
differences)
Made a Type I Error
Reject the null hypothesis
False (there really are
differences)
Made a Correct
Decision
Accept the null hypothesis False (there really are
differences)
Made a Type II
Error
Accept the null hypothesis True (there really are no
differences)
Made a Correct
Decision
Example
•  In the criminal justice system, a defendant is
innocent until proven guilty. Therefore, the null
hypothesis is: “This person is innocent.”
•  In this case, what would be the Type I error?
•  In this case, what would be the Type II error?
•  Which do you think is the more costly error? Why?
5 3/16/14 Effect Size
•  Effect Size (Cohen’s d )
•  The magnitude or size of the experimental treatment.
•  A significant statistical test tells us only that the IV had an effect;
it does not tell us about the size of the significant effect.
•  Cohen (1977) indicated that d values greater than .80 reflect large
effect sizes.
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