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Chapter 13

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McMaster University

Statistics

STATS 2B03

Aaron Childs

Fall

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Stats 2B03: Statistical Methods for Science
Chapter 13: Nonparametric and Distribution-Free Statistics
13.1 Introduction
- Only those procedures that test hypotheses that are not statements about
population parameters are classified as nonparametric, while those that
make no assumption about the sampled population are distribution-free
procedures
- They allow for the testing of hypotheses that are not statements about
population parameter values. Some of the chi-square tests of goodness-of-fit
and the tests of independence are examples of tests possessing this
advantage
- Nonparametric tests may be used when the form of the sampled population
is unknown
- Nonparametric procedures tend to be computationally easier and
consequently more quickly applied than parametric procedures. This can be
a desirable feature in certain cases, but when time is not at a premium, it
merits a low priority as a criterion for choosing a nonparametric test.
- Nonparametric procedures may be applied when the data being analyzed
consist merely of rankings or classifications. That is, the data may not be
based on a measurement scale strong enough to allow the arithmetic
operations necessary for carrying out parametric procedures.
- The use of nonparametric procedures with data that can be handled with a
parametric procedure results in a waste of data
- The application of some of the nonparametric tests may be laborious for
large samples
13.4 The Wilcoxon Signed-Rank Test for Location
- Assumptions:
The sample is random
The variable is continuous
The population is symmetrically distributed about its mean μ
The measurement scale is at least interval
- Hypotheses:
Subtract the hypothesized mean μ from ea0h observation x, to obtain i
d i x i μ .0If any x ii equal to the mean, so that d = 0,ieliminate that d i
from the calculations and reduce n accordingly
Rank the usable d from the smallest to the largest without regard to
i
the sign of d,ithat is consider only the absolute value of the d, i
designated |d|, ihen ranking them. If two or more of the |d| are i
equal, assign each tied value of the mean of the rank positions the tied
values occupy. If, for example, the three smallest |d | are ill equal,
place them in rank pos

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