lecture23 notes

Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Stat 312: Lecture 23 Categorical Data Moo K. Chung [email protected] April 22, 2003 Concepts 1. Multinomial data. There are k outcomes (categories): C 1 , C 2 , ··· , C k . The probabil- ity of sample X i belonging to category C j is p j , i.e. P ( X i C 1 ) = p 1 , ··· , P ( X i C k ) = p k . 2. The null hypothesis of interest is H 0 : p 1 = c 1 , ··· , p k = c k for given constants c 1 , ··· , c k ( c 1 + ··· + c k = 1). H 1 : p j 6 = c j for some j. 3. Let x 1 , ··· , x n be the observations. Sup- pose that there are N j items in category C j . Note that N 1 + ··· + N k = n . We as- sume N 1 , ··· N j to be distributed as multi- nomial with parameter p 1 , ··· , p k . The ex- pected number of elements in category C j is EN j = np j . 4. Chi- squared goodness-of-Ft test. The test procedure involes measuring the relative
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This note was uploaded on 01/31/2008 for the course STAT 312 taught by Professor Chung during the Spring '04 term at Wisconsin.

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