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Unformatted text preview: 1.6 1.6 1.6 1.6 (a) Consider the following statistical model: i i i l y ε τ + + = , i =1,2,…,6, where y i =the i th observed difference between A and B (A-B) τ =the intrinsic difference between A and B (A-B) l i =learning effect of the i th transcript ε i =errors with mean 0 When the test sequence for the i th transcript is AB, B is benefited by the learning effect, thus l i <0. Similarly, l i >0 if the sequence of the i th test is BA. Assume that ... 6 2 1 > = = = = l l l l in part (a). Without randomization, as the following sequence: AB, AB, AB, AB, AB, AB l y − = = η η ˆ , i.e., the estimation of the difference between A and B is biased by l . With randomization as the following sequence: AB, BA, AB, BA, AB, AB 3 6 2 4 ˆ l l l y − = − − = = η η η , i.e., the estimation of the difference between A and B is biased by l /3< l . Using balance in addition to randomization, as the following sequence AB, AB, AB, BA, BA, BA (*) η η η = − − = = 6 3 3 ˆ l l y , i.e., there is no bias if we use balance., i....
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This note was uploaded on 04/26/2011 for the course STATS 424 taught by Professor Peterqian during the Spring '11 term at University of Wisconsin.
- Spring '11