
Interfering factors in the comparison of two sample means
using unpaired samples may inflate the pooled estimate of
variance of test results.

It is possible to pair the measurements.
Only the value of one variable is changed among the
two members of each matched pair, but everything else
is nearly the same (as closely as possible) for the members
of the pairs.

Then the difference between the members of a pair
becomes the important variable, which will be examined by
a ttest.
We test “Is the mean difference significantly different from
zero?”
Statistical Inference for the Mean: ttest
Comparison of paired samples:
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Statistical Inference for the Mean: ttest
Comparison of paired samples:
methods
two
e
between th
difference
real
no
0
:
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=
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H
μ
:
a
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tailed

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μ
test)
tailed

(one
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d
d
μ
μ
Pair No.
1
2
3
4
5
6…
n
Sample A
x
A1
x
A2
x
A3
x
A4
x
A5
x
A6
...
x
An
Sample B
x
B1
x
B2
x
B3
x
B4
x
B5
x
B6
…
x
Bn
d =
x
Ai

x
Bi
x
A1

x
B1
x
A2

x
B2
x
A3

x
B3
x
A4

x
B4
x
A5

x
B5
x
A6

x
B6
…x
An

x
Bn
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 Fall '11
 Glyn
 Math, Statistics, Factors, Normal Distribution, Variance, Statistical hypothesis testing, mean difference

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