Discussion_Ch.11

Discussion_Ch.11 - GB 303 Ch.11 DISCUSSION Doug Bujakowski...

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Unformatted text preview: GB 303 Ch.11 DISCUSSION Doug Bujakowski ANOVA "Factor" = Possible source of variation. Made up of two or more groups. "Block" = Another possible source of variation. We do not care about whether or not block means are different How to decide What does our sample look like? Random (independent) samples: one-way or two-way ANOVA Dependent samples: randomized block One type of factor: one-way ANOVA or randomized block Two types of factors: two-way ANOVA Was H0 for equal groups rejected? Are there 3 or more groups being tested? If both yes, need Tukey(-Kramer). What factor(s) are we testing? Do we use the Tukey(-Kramer) test? !"#$%&'()*)%')+,) ! A Quiz Question from Last Semester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uestion One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olution: ! FJ!! Because we are only looking at one factor (possible differences based on school) FJ! OO 85'!0'9%''#! '%%.% !1'%2!*#!OOOOOOOOOO;! GJ! OOOOOOOOOOOOO! ! ! ! ! GJ! 85'!2'4/!#U$4%'!:.%!15'!1%'412'/1#!*#!OOOOOOOOOO;! ! ! ! "J!DE! ! ! !the !answer will not be !"a!RJ!DKF@B! ! ! ! ! !model".! ! ! ! ! TJ!@! ! ! ! ! RJ!>>! ! ! ! ! "J DEKF@@;AA! ! QJ!DEKFAA;AA! we know ! ! ! !! ! !!! QJ!>A! ! ! ! !!! ! !!! two-factor ! TJ!HFKA>>;>>! ! Because the six students at school one are different than the six students at! CJ! 85'!&4+$'!.:!15'!1'#1!#141*#1*-!:.%!15'!1%'412'/1!'::'-1#!*#!OOOOOOOOOO;! ! ! CJ! OOOOOOOOOOOOO! ! school two,! we! are! !not looking !at! !the same !subjects each time. The answer GJ! 85'!2'4/!#U$4%'!:.%!15'!1%'412'/1#!*#!OOOOOOOOOO;! ! ! GJ! OO ! ! "J!GA! ! ! ! ! ! ! ! QJ!FD;EB! ! ! ! ! ! RJ!G;@BF! ! ! ! ! ! TJ!D;BB! ! ! cannot be "a randomized block model". >BJ! 85'!-%*1*-4+!&4+$'!*/!15'!1'#1!:.%!#*9/*:*-4/1!0*::'%'/-'#!42./9!#-5..+#!41! ! >BJ! ! 15'!#*9/*:*-4/-'!+'&'+!.:!B;BA!*#!OOOOOOOOOOK!#.!)'!OOOOOOOOOO15'!/$++! Answer is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uestion Two ! FJ! 85'!0'9%''#! ! '%%.% !1'%2!*#!OOOOOOOOOO;! ! ! "J!DE! ! ! ! ! ! ! ! ! ! ! QJ!>A! ! ! ! ! ! ! ! ! ! ! ! RJ!>>! ! ! ! ! ! ! ! ! ! TJ!@! ! ! @J! "--.%0*/9!1.!15'!4,.&'!*/:.%241*./K!15'!"LMI"!2.0'+!2.#1!+*N'+(!1.!:*1! ! 15*#!#*1$41*./!*#? "J!4!%4/0.2*P'0!,+.-N!2.0'+;! ! ! QJ!4!1).-:4-1.%!2.0'+;! ! RJ!4!./'S:4-1.%!2.0'+;! ! ! TJ!4++!"LMI"!2.0'+#;! ! FJ! 85'!0'9%''#! ! '%%.% !1'%2!*#!OOOOOOOOOO;! ! ! "J!DE! ! ! ! ! ! ! ! ! ! ! QJ!>A! ! ! ! ! ! ! ! ! ! ! ! RJ!>>! ! ! ! ! ! ! ! ! ! TJ!@! @J! OOOOOOOOOOOOO! ! ! ! FJ! OOOOOOOOOOOOO! ! ! GJ! 85'!2'4/!#U$4%'!:.%!15'!1%'412'/1#!*#!OOOOOOOOOO;! ! ! ! There are 2 ways to find the answer. GJ! ! DEKF@@;AA! !df ! ! QJ!DEKFAA;AA! ! ! for RJ!DKF@B! ! ! ! GJ! OOOOOOOOOOOOO! ! TJ!HFKA>>;>>! "J 85'!2'4/!#U$4%'!:.%!15'!1%'412'/1#!*#!OOOOOOOOOO;! !! !the error = df! total.! Plugging ! The easy way: ! for the treatment + df ! ! "J DEKF@@;AA! ! ! ! QJ!DEKFAA;AA! ! ! RJ!DKF@B! ! ! ! in the numbers! we get 2 + !df! !for the error! !=! TJ!HFKA>>;>>!for the error = 15. 17. So df ! CJ! 85'!&4+$'!.:!15'!1'#1!#141*#1*-!:.%!15'!1%'412'/1!'::'-1#!*#!OOOOOOOOOO;! ! MS. Plugging in ! ! CJ! OOOOOOOOOOOOO! ! CJ! 85'!&4+$'!.:!15'!1'#1!#141*#1*-!:.%!15'!1%'412'/1!'::'-1#!*#!OOOOOOOOOO;! ! The slightly harder but still pretty easy way: SS/df = the numbers ! we ! get 42,400/df != 2760. ! So !df for the error = 15. ! "J!GA! ! ! ! ! ! ! ! ! ! QJ!FD;EB! ! ! ! ! ! ! ! RJ!G;@BF! ! ! ! ! TJ!D;BB! !! ! ! "J!GA! ! ! ! ! ! ! ! ! ! ! ! QJ!FD;EB! ! ! ! ! ! ! ! ! RJ!G;@BF! ! ! ! ! ! ! TJ!D;BB! >BJ! 85'!-%*1*-4+!&4+$'!*/!15'!1'#1!:.%!#*9/*:*-4/1!0*::'%'/-'#!42./9!#-5..+#!41! ! Answer is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uestion Three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se the fact that SS/df = MS. Plugging in the numbers we get >BJ! 85'!-%*1*-4+!&4+$'!*/!15'!1'#1!:.%!#*9/*:*-4/1!0*::'%'/-'#!42./9!#-5..+#!41! CJ! 85'!&4+$'!.:!15'!1'#1!#141*#1*-!:.%!15'!1%'412'/1!'::'-1#!*#!OOOOOOOOOO;! ! CJ! OOOOOOOOOOOOO! ! ! 47511.11/2 = MS for the treatment. So MS for the treatment != 23,755.55 15'!#*9/*:*-4/-'!+'&'+!.:!B;BA!*#!OOOOOOOOOOK!#.!)'!OOOOOOOOOO15'!/$++! ! "J!GA! ! ! ! ! ! ! ! ! ! ! ! QJ!FD;EB! ! ! ! ! ! ! ! ! RJ!G;@BF! ! ! ! ! ! ! TJ!D;BB! !! 5(3.15'#*#;! ! Answer is B >BJ! 85'!-%*1*-4+!&4+$'!*/!15'!1'#1!:.%!#*9/*:*-4/1!0*::'%'/-'#!42./9!#-5..+#!41! ! >BJ!OOOOOOOOOOOOO! ! "J!E;@GK! ! %'V'-1;! ! ! 15'!#*9/*:*-4/-'!+'&'+!.:!B;BA!*#!OOOOOOOOOOK!#.!)'!OOOOOOOOOO15'!/$++! ! %'V'-1! QJ!H;FFK! ! RJ!E;@GK! ! :4*+!1.!%'V'-1! ! 5(3.15'#*#;! ! TJ!H;FFK! ! :4*+!1.!%'V'-1 ! GJ! 85'!2'4/!#U$4%'!:.%!15'!1%'412'/1#!*#!OOOOOOOOOO;! ! ! Solution: DEKF@@;AA! ! ! ! ! QJ!DEKFAA;AA! ! ! ! ! ! RJ!DKF@B! ! ! ! ! ! ! TJ!HFKA>>;>>! "J GJ! OOOOOOOOOOOOO! ! ! "J!E;@GK! ! %'V'-1;! ! ! QJ!H;FFK! ! %'V'-1! ! ! 84,+'!>?!%4)!0414! ! @J! "--.%0*/9!1.!15'!4,.&'!*/:.%241*./K!15'!"LMI"!2.0'+!2.#1!+*N'+(!1.!:*1! ! @J 15*#!#*1$41*./!*#? @AB! A>B! AAB! "J!4!%4/0.2*P'0!,+.-N!2.0'+;! ! ! @DB! @EB! FBB! RJ!4!./'S:4-1.%!2.0'+;! ! @EB! ! AGB! ! F>B! @BB! -./''0)+) -./''0)1) -./''0)2) ACB! Question Four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olution: DEKF@@;AA! ! ! ! !! QJ!DEKFAA;AA! ! ! ! ! ! RJ!DKF@B! ! ! ! ! ! ! TJ!HFKA>>;>>! ! %'V'-1! "J!E;@GK! ! %'V'-1;! ! "J QJ!H;FFK! ! ! F statistic for the treatment = MS treatment/MS error. Using the answer for RJ!CJ! 85'!&4+$'!.:!15'!1'#1!#141*#1*-!:.%!15'!1%'412'/1!'::'-1#!*#!OOOOOOOOOO;! !:4*+!1.!%'V'-1 E;@GK! ! :4*+!1.!%'V'-1! !! TJ!H;FFK! ! ! CJ! OOOOOOOOOOOOO! ! ! question three we get 23755.55/2760 = F stat for the treatment = 8.607. ! "J!GA! ! ! ! ! ! ! ! ! ! ! ! QJ!FD;EB! ! ! ! ! ! ! ! ! RJ!G;@BF! ! ! ! ! ! ! TJ!D;BB! !! ! >BJ Answer is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uestion Five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olution: GJ! 85'!2'4/!#U$4%'!:.%!15'!1%'412'/1#!*#!OOOOOOOOOO;! ! ! GJ! OOOOOOOOOOOOO! ! ! "J DEKF@@;AA! ! ! ! ! QJ!DEKFAA;AA! ! ! ! ! RJ!DKF@B! ! ! ! ! ! ! TJ!HFKA>>;>>! Need to use the alpha=.05 F table for !this. Numerator df is the df for the treatment. ! Denominator df is the df for the error. We find the F critical value = 3.68. CJ! 85'!&4+$'!.:!15'!1'#1!#141*#1*-!:.%!15'!1%'412'/1!'::'-1#!*#!OOOOOOOOOO;! ! ! CJ! OOOOOOOOOOOOO! ! ! Because our F stat !> ! F! critical value! weRJ!G;@BF! !the! null hypothesis and conclude reject ! ! ! ! TJ!D;BB! ! "J!GA! ! ! ! ! ! ! ! ! QJ!FD;EB! ! ! ! ! ! ! ! that ! at least one of the three schools does not have the same mean as the rest. ! Answer >BJ! 85'!-%*1*-4+!&4+$'!*/!15'!1'#1!:.%!#*9/*:*-4/1!0*::'%'/-'#!42./9!#-5..+#!41! ! 2 is A15'!#*9/*:*-4/-'!+'&'+!.:!B;BA!*#!OOOOOOOOOOK!#.!)'!OOOOOOOOOO15'!/$++! 5(3.15'#*#;! ! "J!E;@GK! ! %'V'-1;! ! ! QJ!H;FFK! ! %'V'-1! ! RJ!E;@GK! ! :4*+!1.!%'V'-1! ! TJ!H;FFK! ! :4*+!1.!%'V'-1 ! >BJ!OOOOOOOOOOOOO! ! ! ...
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