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07_RB_1

# 07_RB_1 - Critique of one-way ANOVA Model Yij = j i j...

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Critique of one-way ANOVA Model: ) ( j i j ij Y ε + α + µ = explained (structure) unexplained (error) explained (structure) unexplained (error) Total variation • Structure of the model typically does not account for much of the total variation in the outcome variable. Æ How can we increase the amount of explained part of variation? (i.e., decreasing the unexplained variation) Increasing precision by design: EC 54 43 33 42 10 3.4 2.4 1.52 1.52 j Y j σ ˆ • Standard two-sample t -test (e.g.) 92 . 0 5 1 5 1 ) 52 . 1 ( 1 1 ˆ ˆ 2 1 2 = + = + = j pooled C E n n σ 0 . 1 4 . 2 4 . 3 = = C E Y Y So, 95% CI is . ) 12 . 3 , 12 . 1 ( 12 . 2 1 ) 92 . 0 ( 306 . 2 0 . 1 = ± = ± ( t * α /2 = 0.025, df = 8 = 2.306) • Since the CI contains 0 within its interval, we do not reject the H 0 : µ E - µ C =0 . •O r , t = 1/0.92 = 1.08 (smaller than the critical value)

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• Alternatively, we can conduct a paired t -test: EC d = E - C 541 431 330 422 101 1 0.707 d d σ ˆ 316 . 0 5 707 . 0 ˆ ˆ = = = n d d σ (compare this to ) 92 . 0 ˆ = C E So, 95% CI is . ) 88 . 1 , 12 . 0 ( 88 . 0 1 ) 316 . 0 ( 776 . 2 0 . 1 = ± = ± ( t * α /2 = 0.025, df = 4 = 2.776) • Now, we reject H 0 . How can we explain this? •Or, t = 1/0.316 = 3.16 (larger than the critical value) Randomized Block Design •Create n homogeneous blocks of experimental units. Æ In the matched-pair case, n is the number of pairs (i.e., the number of blocks). Æ p = 2. • Randomly assign each observationunit within a block to one of the treatment levels. Criteria for blocking: • Form sets of subjects who are similar with respect to a nuisance variables. Æ block as a set of homogeneous subjects • Observe each subjects under all of the conditions in the experiment. Æ block as a set of repeated measures
Model: (RB- p design) ) ( j i i j ij Y ε + π + α + µ = where Y ij : observation for block i , treatment j µ : grand mean α j : effect of treatment group

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07_RB_1 - Critique of one-way ANOVA Model Yij = j i j...

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