Statistical Inference for Two Populations
Chapter 7 deals with the methods of statistical inference for comparing parameters of two populations or processes with
respect to their means or their proportions.
We must determine the best statistic for the desired comparison and the sampling distribution of that statistic.
Two basic plans available for this purpose are
:
Independent Samples
and
Paired Samples
Independent samples design
Sample 1
Sample 2
Property
Appraiser 1
Property
Appraiser 2
4
x
7
x
10
x
2
x
1
x
9
x
8
x
6
x
5
x
3
x
__
__
X
1
X
2
__
__
Interested in
X
1
– X
2
where sampling distribution is
_
_
_
_
E(X
1
–X
2
) = E(X
1
) – E(X
2
) = μ
1
 μ
2
__
__
__
__
Var (X
1
– X
2
) = Var (X
1
) + Var (X
2
)
= σ
1
2
/n
1
+ σ
2
2
/n
2
SE (X
1
– X
2
) = √ σ
1
2
/n
1
+ σ
2
2
/n
2
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Paired Samples Design
Appraiser
Property
1
2
Difference
1
x
11
x
21
D
1
2
x
12
x
22
D
2
3
x
13
x
23
D
3
4
x
14
x
24
D
4
5
x
15
x
25
D
5
The paired comparisons analysis reduces to a onesample analysis of the mean of the differences between appraisals.
__
So we are interested in
D
=
∑ D
i
/ n
_
_
where E( D) = μ
d
and Var (D) = σ
d
2
_
Since we would not k
now the value σ
d
2
we would estimate σ
2
with S
2
and hence the standard error of D is
estimated to be SE(D) ≈ S
d
/ √n
Comparison of Independent vs. Paired Samples
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 Spring '09
 CANAVOS
 Normal Distribution, __ X1 Sample

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