STA 4502 Chapter 1

# STA 4502 Chapter 1 - Nonparametric Statistical Methods Yaar...

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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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Stat 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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STA 4502 Chapter 1 - Nonparametric Statistical Methods Yaar...

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