For each combination of response and predictor,
a)What do we want to infer?
b)Which test(s) should we use?
c)What are the assumptions needed?
Response
has a
Normal
Distribution
Response
is
Quantitative but
NONNormal
Distribution
Response
is
Categorical
Predictor
is
Categorical
(Factor)
One Group
μ
= mean response
in the population
η = median response
in the population
p = Proportion of
“Success”s in the
population
p
1
, p
2
, …, p
k
Two
Independent
Groups
μ
1
–
μ
2
= difference
of mean response in
the two populations
η
1
– η
2
= difference of
median response in
the two populations
p
1
– p
2
difference of
proportion of
“Success”s in the two
populations
What if k categories
Matched Pairs
Differences
μ
d
=
μ
1
–
μ
2
= mean
of the population of
differences
η
1
– η
2
= difference of
median response in
the two populations
p
1
– p
2
difference of
proportion of
“Success”s in
dependent populations
Several Groups
i
j
μ
μ

=
differences of mean
responses in the
g(g–1)/2 pairs of
populations
i
j
η
η

= differences
of mean responses in
the g(g–1)/2 pairs of
populations
Differences of the
distribution
of response
between populations
or
association between
two categorical
variables.
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 Summer '08
 Kyung
 Statistics, Normal Distribution, Statistical tests, Nonparametric statistics, Predictor

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