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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 ... TwoSample 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 Distributionfree 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 ......
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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.
 Fall '09
 Frade

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