Lecture05

Lecture05 - Possible Course Flow Estimating success...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Possible Course Flow Estimating success probabilities Single location: estimates, tests, intervals Two locations: testing, estimating differences between locations Scale comparisons and others Multiple locations and factors Independence Nonparametric regression Other topics ... Two-Sample Problem Compare two population centers via locations (medians) Now, compare scale parameters Perhaps same location, perhaps not Even more generally, compare two distributions in all respects Assumptions X i , i = 1 , 2 ,..., m iid Y i , i = 1 , 2 ,..., n iid N = m + n observations X i ’s and Y i ’s are independent Continuous populations F is distribution of X , population 1 G is distribution of Y , population 2 Ansari - Bradley Test Distribution-free Ranks again Null: H : F ( t ) = G ( t ) for all t Same distribution (but no specified) Assume same median θ 1 = θ 2 Ansari - Bradley Test Interested in knowing if one distribution has different variability than the other Suppose F ( t ) = H t- θ 1 η 1 G ( t ) = H t- θ 2 η 2 Equivalently: X d = η 1 Z + θ 1 , Y d = η 2 Z + θ 2 , with Z ∼ H H is continuous with median 0 ⇒ F ( θ 1 ) = G ( θ 2 ) = 1 / 2 Further assumption: θ 1 = θ 2 (common median) In summary, X- θ η 1 d = Y- θ η 2 If θ 1 6 = θ 2 , but both are known , shift each sample: X i = X i- θ 1 , Y i = Y i- θ 2 . Now have common median 0 Ansari - Bradley Test Look at ratio of scales: γ = η 1 /η 2 If variances exist for X and Y , then γ 2 = var( X ) var( Y ) Write null as H : γ 2 = 1 Ansari - Bradley Test Order the N combined sample values Assign 1 to smallest and largest Assign 2 to next smallest and next largest Continue ......
View Full 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 / 34

Lecture05 - Possible Course Flow Estimating success...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online