Statistical Inference: Lecture 17 - Hypothesis Testing: Multinomial & Two Sample Tests, Study notes of Statistics

Download Statistical Inference: Lecture 17 - Hypothesis Testing: Multinomial & Two Sample Tests and more Study notes Statistics in PDF only on Docsity! 1 STAT 703/J703 B.Habing Univ. of SC 1 STAT 703/J703 March 20th, 2007 -Lecture 17- Instructor: Brian Habing Department of Statistics LeConte 203 Telephone: 803-777-3578 E-mail: habing@stat.sc.edu STAT 703/J703 B.Habing Univ. of SC 2 Today • Example 1: Test for a Multinomial Distribution • Example 2: Two Sample Tests for Location STAT 703/J703 B.Habing Univ. of SC 3 Example 1: Consider a data set that could have come from a binomial distribution with n=5, but may also have come from a hypergeometric or some other distribution. X 0 1 2 3 4 5 #obs 9 21 16 10 4 0 Test H0: X is binomial vs. HA: it isn’t 2 STAT 703/J703 B.Habing Univ. of SC 4 So in general we get ∑ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ =Λ−= = n i i i i E OOG 1 2 log2log2 STAT 703/J703 B.Habing Univ. of SC 5 Page 342-343 demonstrates that this is asymptotically the same as the classic ( ) ∑ − = n i i ii E EO 1 2 STAT 703/J703 B.Habing Univ. of SC 6 Theorem A pg.310: Under smoothness conditions on the pdf, the null distribution of –2lnΛ has an approximate chi-square distribution with d.f.=dimΩ-dimω0 for large n.