lecture04

# lecture04 - Possible Course Flow Estimating success...

This preview shows pages 1–8. Sign up to view the full content.

Possible Course Flow Estimating success probabilities Single location: estimates, tests, intervals Two locations: testing, estimating diﬀerences between locations Scale comparisons Multiple locations and factors Independence Nonparametric regression Other topics . ..

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Location Compare two population centers Location diﬀerences (only) Now, two distinct populations (data not paired)
Assumptions X i , i = 1 , 2 , . . . , m iid F (population 1) Y i , i = 1 , 2 , . . . , n iid G (population 2) N = m + n observations X i ’s and Y i ’s are independent Continuous populations

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Wilcoxon (Mann-Whitney) Test Distribution-free Some assumptions (continuous, iid) Null: H 0 : F ( t ) = G ( t ) for all t Same distribution
Wilcoxon (Mann-Whitney) Test Usually interested in a shift of one distribution with respect to the other X F . Let X 0 = X + Δ. What is the distribution of X 0 ? Location shift model ( assumption ): G ( t ) = F ( t - Δ) for all t Or Y d = X + Δ Δ is location shift or treatment eﬀect If E ( X ) and E ( Y ) exist Δ = E ( Y ) - E ( X ) H 0 : G ( t ) = F ( t ) vs. H 1 : G ( t ) = F ( t - Δ) with Δ >, <, 6 = 0. Or H 0 : Δ = 0 vs. H 1 : Δ >, <, 6 = 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Wilcoxon (Mann-Whitney) Test Rank the N (= m + n ) combined samples Denote the ranks of Y within this ranking as S i W = n j =1 S j = n j =1 rank ( Y j ) Rank-sum test
One-tail alternative H 1 : Δ > 0 Reject H 0 if W w α Table A.6 Assumes Y is the smaller sample size ( n m ) n ( n + 1)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/16/2011 for the course STAT 5407 taught by Professor Frade during the Fall '09 term at FSU.

### Page1 / 30

lecture04 - Possible Course Flow Estimating success...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online