Chapter 2: TwoSample Methods
8 Selecting Among TwoSample Tests
•
Assumptions
–
X
1
, . . . , X
m
∼
iid
F
1
and
Y
1
, . . . , Y
n
∼
iid
F
2
(
F
1
and
F
2
are continuous cumulative distribution)
–
X
1
, . . . , X
m
and
Y
1
, . . . , Y
n
are independent
–
: the cdf’s differ by
△
F
1
(
x
) =
F
2
(
x
− △
)
•
Testing
H
0
:
△
= 0
•
The ttest
–
if
F
1
and
F
2
are normal with equal variance
–
the correct probability of a Type I error and the greatest power
–
modest violations of the normality assumption have little effect on the
probability of a Type I error of the ttest
–
the robustness property for the probability of a Type I error: due to
the CLT effect
∗
5 to 10 samples from Uniform distribution
∗
around 20 sample from Exponential distribution
–
when the underlying distributions are normal, the theoretical support
for the optimality in terms of power
•
The Wilcoxon RankSum Test vs. the tTest
–
Wilcoxon Test
∗
advantages over the ttest, when the observations are usually large
or small in comparison with the rest the data
∗
greater power for moderate to large samples and for distributions
that are heavier tailed or skewed
∗
may be preferred on the basis of Type I error considerations
–
the ttest
∗
greater power than the Wilcoxon test for small samples and for
distributions that are lighttailed
∗
validity might be in question for very small sample, when sampling
is from nonnormal distribution but the table critical values are
used .
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
•
Relative Efficiency
–
Two test ar the same level of significance
–
m
1
+
n
1
=
N
1
m
2
+
n
2
=
N
2
with
m
1
/n
1
=
m
2
/n
2
–
choose
N
1
and
N
2
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Staff
 Statistics, Normal Distribution, Variance, Nonparametric statistics, Wilcoxon, Wilcoxon ranksum test

Click to edit the document details