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Paired t -test: t DI. Introduction To The Repeated
Measures Design:What is a
repeated measure?II. Finding an Experimental Effect In
a Single Group: Before vs. After
III. Creating a new distribution t D.IV. Reduces Sampling Error:
Its a
more powerful test
V. Limited Applicability
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Anthony Greene 3
It doesnt have to be Before-After
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Anthony Greene 4
Matched Subject DesignFor a given study the two groups of
subjectscould be closely matched1. Age2. IQ3. Blood Pressure4.
Income5. Education Level
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Anthony Greene 5
The Basic IdeaStandard t-test
n x1 x22 6
13 17
24 28
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Anthony Greene 6
The Basic IdeaStandard t-test
n x1 x22 6
13 17
24 28average 13 17
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The Basic IdeaStandard t-test
Is 13 different than 17? Or 13-17 different than 0?
n x1 x22 6
13 17
24 28average 13 17
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The Basic IdeaRepeated Measures t-test
n x1 x2A 2 6
B 13 17
C 24 28
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The Basic IdeaRepeated Measures t-test
Create A New Variable, D
n x1 x2 DA 2 6 4
B 13 17 4
C 24 28 4
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The Basic IdeaRepeated Measures t-test
Is 4 different than 0?
subject x1 x2 DA 2 6 4
B 13 17 4
C 24 28 4average 4
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The Basic Idea
Are there limitations?
The repeated measure design (before after) must be
used cautiously used in many experimental designs1. Memory
Subjects learn2. Medicine and Clinical Psych Substantial time
passes
3. Social Psych Minor deceptions
Loss of half the degrees freedom
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Distribution of the Paired
t -StatisticSuppose x is a variable on each of two populations
whosemembers can be paired. Further suppose that the
paired-differencevariable 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 D = 0
D
D D
M
M D
D
M D
s
M
n s
M t
QQ !!
/
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The paired t -test for two
population means (Slide 1 of 3)Step 1 The null hypothesis is H 0
: Q D = 0; the alternativehypothesis is one of the following:
H a : Q D
{ 0 H a : Q D
< 0 H a : Q D
> 0
(Two Tailed) (Left Tailed) (Right Tailed)
Step 2 Decide on the significance level, E
Step 3 The critical values aret E / 2 -t E + t E
(Two Tailed) (Left Tailed) (Right Tailed)
with df = n - 1.
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Anthony Greene 15
The paired t -test for two
population means (Slide 2 of 3)
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Anthony Greene 16
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 therejection
region, reject H 0 , otherwise do notreject H 0 .
0normallywhere
/
!
!!
D
D
D D
M
D Dn s
M
s
M t
D
Q
QQ
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The number of doses of medication needed for asthma attacks
before and after relaxation training.
72.3592.1
2.3
92.14
8.141
!!!
!!!
D M
D
D
s
M t
nSS
s
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A Direct Comparisonx1 x2 t -test: Two-Sample
25.7 24.9
20 18.8 Variable 1 Variable 2
28.4 27.7 Mean
18.91 18.25
13.7 13 V ariance 55.83211 55.0383318.8 17.8 Ob servations 10
1012.5 11.3 P ooled V ariance 55.4352228.4 27.8 df 18
8.1 8.2 Standard Error 1.754917
23.1 23.1 t stat 0.19821510.4 9.9 t critical two-tail
2.100924
x1 x2
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A Direct Comparisonx1 x2 D
25.7 24.9 0.8 t -test: P aired20 18.8 1.2
28.4 27.7 0.7 Variable 1 Variable 2 13.7 13 0.7 M ean 18.91
18.2518.8 17.8 1 V ariance 55.83211 55.0383312.5 11.3 1.2 Ob
servations 10 1028.4 27.8 0.6 df 9
8.1 8.2 -0.1 Standard Error of D 0.14
23.1 23.1 0 t stat 4.71428610.4 9.9 0.5 t crit two-tail
2.262159
x1 x2
