caffeine - Randomized Block Design Caffeine and Endurance...

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Randomized Block Design Caffeine and Endurance in 9 Bicyclists W.J. Pasman, et al. (1995). “The Effect of Different Dosages of Caffeine on Endurance Performance Time,” International Journal of Sports Medicine , Vol. 16, pp225-230
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Randomized Block Design (RBD) t > 2 Treatments (groups) to be compared b Blocks of homogeneous units are sampled. Blocks can be individual subjects. Blocks are made up of t subunits Subunits within a block receive one treatment. When subjects are blocks, receive treatments in random order. Outcome when Treatment i is assigned to Block j is labeled Y ij • Effect of Trt i is labeled α i • Effect of Block j is labeled β j • Random error term is labeled ε ij Efficiency gain from removing block-to-block variability from experimental error
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Randomized Complete Block Designs Model (Block effects and random errors independent): ( 29 ( 29 2 2 1 , 0 ~ , 0 ~ 0 e ij b j t i i ij j i ij j i ij N N Y σ ε β α μ = + + = + + + = = Test for differences among treatment effects: H 0 : 1 = ... = t = 0 ( 1 = ... = t ) H A : Not all i = 0 (Not all i are equal) Typically not interested in measuring block effects (although sometimes wish to estimate their variance in the population of blocks). Using Block designs increases efficiency in making inferences on treatment effects
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RBD - ANOVA F -Test (Normal Data) Data Structure: ( t Treatments, b Subjects/Blocks) Mean for Treatment i : Mean for Subject (Block) j : Overall Mean: Overall sample size: N = bt ANOVA: T reatment, B lock, and E rror Sums of Squares . i y j y . .. y ( 29 ( 29 ( 29 ( 29 ) 1 )( 1 ( 1 1 1 2 .. . . 1 2 .. . 1 2 .. . 1 1 2 .. - - = - - = + - - = - = - = - = - = - = - = ∑∑ ∑ ∑ = = = = t b df SSB SST TSS y y y y SSE b df y y t SSB t df y y b SST bt df y y TSS E j i ij B b j j T t i i t i b j Total ij
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RBD - ANOVA F -Test (Normal Data) ANOVA Table: Source
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This note was uploaded on 06/04/2011 for the course STA 6166 taught by Professor Staff during the Fall '08 term at University of Florida.

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caffeine - Randomized Block Design Caffeine and Endurance...

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