Download - Difference Between Means
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Learning ObjectivesIn this chapter you will learn
about the t-test and its distributiont-test for related samplest-test for independent samples
hypothesis testinghow to use SPSS to test for differences between means
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t DistributionIn Chapter 6, you were
introduced to the Normal Distribution
In this chapter, we will explore another distribution– t distribution
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t DistributionIf the sample size is less than 30
–use the t distribution•to calculate confidence intervals
–as sample size increases•t distribution approximates the normal
distribution•the shape of t distribution is not fixed
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Hypothesis TestingHypothesis testing•based on sample evidence
and probability theory•used to determine whether
the hypothesis should or should not be rejected
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Important TermsNull Hypothesis• A statement about the expected
value of a population parameterAlternative Hypothesis• Research statement that is
accepted– if the sample data suggest that the
null hypothesis should be rejected
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Type I & Type II Errors
Type I Error•Rejecting the null hypothesis
when it is actually trueType II Error () •Accepting the null hypothesis
when it is actually false
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Type I ErrorsThe chance of making a Type I
error is known as the level of significance or the alpha level ()– it is set by the researcher– the convention is to use the .05
level of significance as the probability of committing Type I error
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Steps in Hypothesis Testing
One-tailed or two-tailed test?
Do not reject null Reject null and accept alternative
Step 5: Reach a decision
Step 4: Collect and analyze data
Step 3: Identify appropriate statistic
Step 2: Select a level of significance
Step 1: State null and alternative hypotheses
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The Null HypothesisThe research hypothesis is not tested directly– Instead, we test the null hypothesis
(H0): the hypothesis of no difference or no relationship
– We can never prove a hypothesis to be true
– Instead, we are searching for instance when it is not true
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Accept or Reject?Compare the test statistic (obtained value) to the alpha level and decide if it is greater or less than alpha– if less than, reject H0
– if greater than, retain H0
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Decisions Under the Null HypothesisDecision H0 is True H0 is False
Reject H0
Type I Error Correct
Accept H0
Correct Type II Error
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t TestWe frequently want to
compare means–different tests based on sample•paired t test for related sample•independent t test when samples
are not related somehow
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SPSS ProcedureThe following slides
demonstrate the independent t test–don’t forget to
•test for equality of variance•define the group either by specifying a
group number (discrete variable) or by using the cut point (perhaps the median) if the variable is continuous
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SPSS Step 1
Open data set
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SPSS Step 2
Select Compare Means and then Independent Samples T Test
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SPSS Step 3
Select the test variable and then the grouping variable
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SPSS Step 4
Define the groups or use the Cut Point to divide a continuous-level variable
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SPSS Step 5
Mouse Click OK to obtain results
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SPSS Output