Lecture05

Lecture05 - Possible Course Flow Estimating success...

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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 ... 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 ......
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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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Lecture05 - Possible Course Flow Estimating success...

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