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Unformatted text preview: Estimability Example An education major wanted to test the efficacy of teaching methods for the division of fractions. Two new methods along with the standard method were studied. Five teachers were trained in all methods and taught a total of twelve classes. Differences in pre and posttest scores are recorded below: Teacher Method 1 2 3 4 5 A 10 , 7 6 11 6 B 4 5 7 , 8 3 C 13 16 Our model is: Y ijk = μ ij + ijk , i = 1 , 2 , 3; j = 1 , 2 , 3 , 4 , 5; k = 1 , . . . , n ij , where μ ij = μ + α i + β j + γ ij The population marginal mean for Method A would be: PMM ( α 1 ) = 1 5 ( μ 11 + μ 12 + μ 13 + μ 14 + μ 15 ) = μ + α 1 + 1 5 ( β 1 + β 2 + β 3 + β 4 + β 5 ) + 1 5 ( γ 11 + γ 12 + γ 13 + γ 14 + γ 15 ) Remember that this is the parameter that LSMEANS( α 1 ) would estimate. To find out whether or not this parameter is estimable in the interaction model (of course, we know it’s not since there is no entry for cell μ 14 ), we ask SAS for the general form of estimable...
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 Spring '08
 JohnM.Grego
 Subroutine, ijk, population marginal mean

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