Paired t-test: tD

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Paired t-test tD

1. Introduction To The Repeated Measures DesignWhat
   is a repeated measure?
2. Finding an Experimental Effect In a Single Group
   Before vs. After
3. Creating a new distribution tD.
4. Reduces Sampling Error Its a more powerful
   test
5. Limited Applicability

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Before-After
Pre-Measure
Post-Measure
Manipulation
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It doesnt have to be Before-After
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Matched Subject Design

• For a given study the two groups of subjects
  could be closely matched
• Age
• IQ
• Blood Pressure
• Income
• Education Level

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The Basic Idea

• Standard t-test

n x1 x2
2 6
13 17
24 28

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The Basic Idea

• Standard t-test

n x1 x2
2 6
13 17
24 28
average 13 17
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The Basic Idea

• Standard t-test
• Is 13 different than 17? Or 13-17 different than
  0?

n x1 x2
2 6
13 17
24 28
average 13 17
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The Basic Idea

• Repeated Measures t-test

n x1 x2
A 2 6
B 13 17
C 24 28

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The Basic Idea

• Repeated Measures t-test
• Create A New Variable, D

n x1 x2 D
A 2 6 4
B 13 17 4
C 24 28 4

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The Basic Idea

• Repeated Measures t-test
• Is 4 different than 0?

subject x1 x2 D
A 2 6 4
B 13 17 4
C 24 28 4
average 4
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The Basic Idea

• The fundamental advantage?
• The error term in the within subjects design is
  smaller
• In the simplified example, the standard error
  terms would be higher in the two sample version
  versus the difference test (in this case the sMD
  is zero)
• The advantage is that individual differences (2,
  13, 24, and 5, 16, 27) are not part of the error
  in tD

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The Basic Idea

• Are there limitations?
• The repeated measure design (before after) must
  be used cautiously used in many experimental
  designs
• Memory
  Subjects learn
• Medicine and Clinical Psych Substantial time
  passes
• Social Psych Minor
  deceptions
• Loss of half the degrees freedom

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Distribution of the Paired t-Statistic
Suppose x is a variable on each of two
populations whose members can be paired. Further
suppose that the paired-difference variable D is
normally distributed. Then, for paired samples of
size n, the variable has the t-distribution
with df n 1. The normal null hypothesis is
that µD 0
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The paired t-test for two population means (Slide
1 of 3)
Step 1 The null hypothesis is H0 ?D 0 the
alternative hypothesis is one of the
following Ha ?D ? 0 Ha ?D lt 0 Ha ?D gt
0 (Two Tailed) (Left Tailed) (Right
Tailed) Step 2 Decide on the significance level,
? Step 3 The critical values are t?/2 -t? t?
(Two Tailed) (Left Tailed) (Right Tailed) with
df n - 1.
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The paired t-test for two population means (Slide
2 of 3)
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The paired t-test for two population means(Slide
3 of 3)
Step 4 Compute the value of the test
statistic Step 5 If the value of the test
statistic falls in the rejection region, reject
H0, otherwise do not reject H0.
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The number of doses of medication needed for
asthma attacks before and after relaxation
training.
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A Direct Comparison
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A Direct Comparison