Stat 4502 Chap 1, Page 1 of 6
Nonparametric
Statistical
Methods
Yaşar Yeşilçay
These notes are based on those prepared by
P
ROFESSOR
R
ONALD
H.
R
ANDLES
With Some Portions prepared by
Professor Dennis Wackerly
Fall 2011
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View Full DocumentStat 4502 Chap 1, Page 2 of 6
Chapter 1
Preliminaries
One of the most important activities of an applied statistician is making statistical inference (
1
),
i.e., making statements about one or more characteristics of a population of interest, based on a
random sample (
2
).
In the prerequisite (
3
) you took for this course you have seen a large number of inferential
techniques. Among these, when the response variable (Y) is quantitative, we always assumed
that the population has a normal distribution, i.e., Y ~ N(μ, σ).
However, in many real life problems this assumption does not hold and it becomes extremely
important when the sample size is small. (This is especially true in many medical studies.)
An alternative is to use a set of inferential techniques known as nonparametrics or distribution
free statistics.
Nonparametric methods are procedures that are not based on the fact that the population
has a specific distribution (e.g., Normal).
Nonparametric methods have the following characteristics:
Assumptions about the population are less restrictive.
Easy to apply.
Easy to understand and interpret
Institutive distribution theory
Use simplified sample statistics
Work well even if normal theory methods are applicable.
Have good
EFFICIENCY.
Read 1.1 to see other advantages of nonparametric methods.
1
Statistical inference
is the process of making a statement about a population (more
specifically, about one or more parameters of a population) based on data from a random
sample.
2
The simplest random sample, called
Simple Random Sample
(SRS), is one that is selected in
such a way that all possible samples of a fixed size (n) from that population have equal
probability of being selected. This yields a sample where every unit in the population has the
same probability of being selected.
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 Summer '11
 YESILCAY
 Statistical hypothesis testing, population median

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