The ranking procedure described in Exercise 45 is
somewhat asymmetric, because the smallest observation receives rank 1 whereas the largest receives
rank 2, and so on. Suppose both the smallest and the
largest receive rank 1, the second smallest and second largest receive rank 2, and so on, and let ...
Suppose we wish to test
H0: the X and Y distributions are identical
: the X distribution is less spread out than the
The accompanying gure pictures X and Y distributions for which H
a is true. The Wilcoxon rank-sum
test is not appropriate in this situation because when
In an experiment to study the way in which different
anesthetics affect plasma epinephrine concentration, ten dogs were selected and concentration was
measured while they were under the in uence of the
anesthetics iso urane, halothane, and cyclopropane
( Sympathoadrenal and Hemodynamic Effects of
The model for the data from a randomized block experiment for comparing I treatments was Xij m
ai bj eij, where the a s are treatment effects, the
b s are block effects, and the e s were assumed normal with mean 0 and variance s2. We now replace
normality by the assumption that the e s have t...
The single-factor ANOVA model considered in
Chapter 11 assumed the observations in the ith
sample were selected from a normal distribution
with mean mi and variance s2, that is, Xij mi eij
where the e s are normal with mean 0 and variance
s2. The normality assumption implies that the F
test is no...
Refer to Exercise 39, and consider a con dence interval associated with the sign test, the sign interval. The relevant hypotheses are now H0:
a: . Let s use the following rejection
region: either Y 15 or Y 5.
a. What is the signi cance level for this test?
b. The con dence interval will c...
The sign test is a very simple procedure for testing
hypotheses about a population median assuming
only that the underlying distribution is continuous.
To illustrate, consider the following sample of 20 observations on component lifetime (hr):...