MidtermReview1

# MidtermReview1 - Applied Nonparametrics STA 4502/5507...

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Applied Nonparametrics STA 4502/5507 Yiyuan She Department of Statistics, Florida State University Fall 2009

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Midterm Review Estimating success probabilities Single location: estimates, tests, intervals Two locations: testing, estimating diﬀerences between locations Scale comparisons and others
Problems replicates data ) Two sample location diﬀerence Two sample scale diﬀerence Distribution comparison (goodness of ﬁt)

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Methods Rank/sign tests: ranks, signs Fisher sign test, Wilcoxon signed rank test Wilcoxon rank sum test, robust rank test Ansari-Bradley test Jackknife Goodness of ﬁt test: Kolmogorov-Smirnov
Binomial Test Some basic concepts: Type-I error, Type-II error, Power; point estimate, conﬁdence interval Critical value method for hypothesis testing (use the quantile function in R ) p -value: smallest signiﬁcance level at which we would reject the null based on the given data (use the distribution function in R ) p -value methods is more informative (why?)

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Exact Binomial Test X 1 , X 2 , ··· , X n Bernoulli( p ) Consider H 0 : p = p 0 Test statistic: B = X i Null distribution B Bin ( n , p 0 ) Rejection region
Large Sample Test B is asymptotically normal (CLT) This test will be approximate (OK for large samples) Under H 0 : E ( B ) = np 0 var( B ) = np 0 (1 - p 0 ) Standardize B B * = B - np 0 p np 0 (1 - p 0 ) B * approximately normal(0, 1) Critical values are now z α

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Estimation Point estimate for p : ˆ p = B / n Conﬁdence interval: p L ( α ) = ˆ p - z α/ 2 p ˆ p (1 - ˆ p ) / n , p U ( α ) = ˆ p + z α/ 2 p ˆ p (1 - ˆ p ) / n Asymptotic method, based on P - z α/ 2 < p - ˆ p p p (1 - p ) / n < z α/ 2 ! = 1 - α binom.test
Wilcoxon Signed Rank Test Paired replicates data Distribution-free ( X , Y ) What are the assumptions? (pairs, continuity, symmetry, independence) Null: H 0 : θ = 0 No diﬀerence before and after

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Set ψ i = 1 , Z i > 0 , 0 , Z i < 0 . Get ranks
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## This note was uploaded on 12/16/2011 for the course STAT 5407 taught by Professor Frade during the Fall '09 term at FSU.

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MidtermReview1 - Applied Nonparametrics STA 4502/5507...

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