Transcript Repeated Measure Experiment, or Related/Paired Sample t

t-Static
1. Single Sample or One Sample t-Test
AKA student t-test.
2. Two Independent sample
t-Test, AKA Between Subject Designs or
Matched subjects Experiment.
3. Related Samples t-test or Repeated
Measures Experiment AKA Within
Subject Designs or Paired Sample TTest .
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CHAPTER 11
Repeated Measure
Experiment,
Related/Paired Sample
t-test or, Within Subject
Experiment Design
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Repeated Measure Experiment, or
Related/Paired Sample t-test Within
Subject Experiment Design
 A single sample of individuals
is measured more than once
on the same dependent
variable. The same subjects
are used in all of the treatment
conditions.
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Null Hypothesis
 t-Statistics:
 If the Population mean or µ is unknown
the statistic of choice will be t-Statistic
 Repeated Measure Experiment, or
Related/Paired Sample t-test
 If non-directional or two tailed test, then
 Step. 1
 H0 :
 H1 :
µD = 0
µD ≠ 0
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Null Hypothesis
 t-Statistics:
 If directional or one tailed tests
 Step. 1
 H0 :
 H1 :
µD ≤ 0
µD > 0
or, Step. 1
 H0 :
 H1 :
µD ≥ 0
µD < 0
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None-directional Hypothesis Test
STEP 2
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Calculations for t-test
Step 3: Computations/ Calculations or Collect
Data and Compute Sample Statistics
MD-μD
t=
SMD
SM
SM
D
= S/√n or
D
=
2
S /n
MD-μD
t
MD = t.SM + μD
D
μD = MD- SM .t
D
SMD = Estimated Standard Error of the mean difference
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Calculations for t-test
Step 3: Computations/ Calculations or Collect
Data and Compute Sample Statistics
df=n-1
Difference Score
MD
=
D= X -X1
2
ΣD
n
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FYI
Variability
SS, Standard Deviations and Variances
 X
1
2
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σ² = ss/N
σ = √ss/N
Pop
s = √ss/df
s² = ss/n-1 or ss/df
SS=Σx²-(Σx)²/n new 
Sample
SS=ΣD²-(ΣD)²/n
SS=Σ( x-μ)²
Sum of Squared Deviation from Mean
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Cohn’s d=Effect Size for t
Use S instead of σ for t-test
 d = MD/s
 S= MD/d
 MD= d . s
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Percentage of Variance
Accounted for by the Treatment
(similar to Cohen’s d) Also
known as ω² Omega Squared
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t
2
r  2
t  df
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Problems
Research indicates that the color red
increases men’s attraction to
women (Elliot & Niesta, 2008). In
the original study, men were shown
women’s photographs presented
on either white or red background.
Photographs presented on red were
rated significantly more attractive than
the same photographs mounted on white.
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Problems
In a similar study, a researcher
prepares a set of 30 women’s
photographs, with 15 mounted
on a white background and 15
mounted on red. One picture is
identified as the test
photograph, and appears twice
in the set, once on white and
once on red.
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Problems
 Each male participant looks through the entire
set of photographs and rated the attractiveness
of each woman on a 12-point scale. The data
in the next slide summarizes the responses for
a sample of n=9 men.
 Set the level of significance at α=.01
for two tails
Do the data indicate the color red
increases men’s attraction to women ?
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Problems
Participants White background X1 Red Background X2 D=X2-X1
A
6
9
+3
B
8
9
+1
C
7
10
+3
D
7
11
+4
E
8
11
+3
F
6
9
+3
G
5
11
+6
H
10
11
+1
I
8
11
+3
D²
9
1
9
16
9
9
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1
9
ΣD =27 ΣD²=99

D
MD =
n
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Null Hypothesis
 For Non-Directional or two tailed tests
Step. 1
H0 : µ = 0
H1 : µ ≠ 0
D
D
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None-directional Hypothesis Test
STEP 2
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Calculations for t-test
Step 3: Computations/ Calculations or Collect
Data and Compute Sample Statistics
MD-μD
t=
SMD
SM
SM
D
= S/√n or
D
=
2
S /n
MD-μD
t
MD = t.SM + μD
D
μD = MD- SM .t
D
SMD = Estimated Standard Error of the mean difference
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Problems
One technique to help people deal with phobia
is to have them counteract the feared objects
by using imagination to move themselves to a
place of safety. In an experiment test of this
technique, patients sit in front of a screen and
are instructed to relax. Then they are shown a
slide of the feared object for example, a picture
of a spider, (arachnophobia). The patient
signals the researcher as soon as feelings of
anxiety begin to arise, and the researcher
records the amount of time that the patient was
able to endure looking at the slide.
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Problems
 The patient then spends two minutes
imagining a “safe scene” such as a tropical
beach (next slide) before the slide is presented
again. If patients can tolerate the feared object
longer after the imagination exercise, it is
viewed as a reduction in the phobia. The data in
next slide summarize the items recorded from a
sample of n=7 patients.
 Do the data indicate the imagination
technique effectively alters phobia?
 Set the level of significance at α=.05 for one
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tailed test.
Problems
Participant Before imagination X1 After Imagination X2 D=X2-X1
D²
A
15
24
+9
81
B
10
23
+13
169
C
7
11
+4
16
D
18
25
+7
49
E
5
14
+9
81
F
9
14
+5
25
G
12
21
+9
81
ΣD =56 ΣD²=502
MD =
D
n
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Null Hypothesis
 For Directional or one tailed tests
 Step. 1
H : µ ≤0
H : µ >0
0
D
(The amount of time is not increased.)
1
D
(The amount of time is increased.)
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FYI Hypothesis Testing
Step 2: Locate the Critical Region(s) or
Set the Criteria for a Decision
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Calculations for t-test
Step 3: Computations/ Calculations or Collect
Data and Compute Sample Statistics
MD-μD
t=
SMD
SM
SM
D
= S/√n or
D
=
2
S /n
MD-μD
t
MD = t.SM + μD
D
μD = MD- SM .t
D
SMD = Estimated Standard Error of the mean difference
2
7
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Chapter 12
Estimation
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