Lecture02

# Lecture02 - Applied Nonparametrics STA 4502/5507 Yiyuan She...

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Unformatted text preview: Applied Nonparametrics STA 4502/5507 Yiyuan She Department of Statistics, Florida State University Fall 2009 Possible Course Flow Estimating success probabilities Single location: estimates, tests, intervals Two locations: testing, estimating di erences between locations Scale comparisons Multiple locations and factors Independence Nonparametric regression Other topics ... Binomial Test Observe outcomes of n trials Assumptions Independent Success / failure Identical Test H : p = p p a speci ed value in (0, 1) Use a test statistic B = number of successes Binomial Test One-sided alternative H 1 : p &amp;gt; p For a speci ed level of signi cance , get critical value b = P (reject H j H true) = Type I error Table A.2 in NSM or pbinom in R Reject H if B b Binomial Test One-sided alternative H 1 : p &amp;lt; p For a speci ed level of signi cance , get critical value c Reject H if B c If p = 1 = 2, symmetry gives c = n b Binomial Test Two-sided alternative H 1 : p 6 = p Reject H if B b 1 or B c 2 = 1 + 2 Usually, 1 = 2 = = 2 Binomial Test pbinom(q, size, prob, lower.tail=T) pbinom(2, 5, 0.4, lower.tail=T) is P ( B 2) where there are n = 5 trials and success probability is 0.4 pbinom(2, 5, 0.4, lower.tail=F) is P ( B &amp;gt; 2) = 1 P ( B 2) Note P ( B &amp;gt; 2) = P ( B 3) Default is lower.tail=T Binomial Test ?pbinom for documentation Density, distribution function, quantile function and random generation for the binomial distribution with parameters size...
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Lecture02 - Applied Nonparametrics STA 4502/5507 Yiyuan She...

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