05_Mult Comp_3

05_Mult Comp_3 - Dunn-Sidak Test - simply Sidak in SPSS A...

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Dunn-Sidak Test -- simply “Sidak” in SPSS • A modification of Bonferroni procedure. • Slightly more liberal than Bonferroni narrower confidence intervals, and more powerful . • In Bonferroni the modified α -level is: α /2 C (e.g.) 005 2 2 0 0125 ./ . = • In Dunn-Sidak the modified α -level is: 11 2 1 −− (/ ) α C (e.g.) 2 110 0 5 2 1 1 0 025 0 0134 1 12 05 =−− =− − = ) ( . / ) (. ) . / . α C t df α * ., * . == = 0 0125 12 256 So, t df α * * . = 00134 252 So, Dunnet’s Procedure (pp.134-137) • Another planned comparisons (Case 2). • Compares one group versus each one of the rest of p -1 groups, i.e., p - 1 non-orthogonal contrasts. (e.g.) control group vs. treatment groups • Technically, the procedure is applicable to any set of p - 1 planned non-orthogonal contrasts, where correlation between any two contrasts is 0.5. (example) ψµ µ µ 21 3 32 3 = =− (The same example in Bonferroni) • Use the same and , i.e., the same t -statistic. • However, use a different critical value, based on Table E.7. i ψ ˆ i ψ σ ˆ
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(example) , 3 2 3 3 1 2 µ µ = ψ µ µ = ψ t 2 = 1.13 t 3 = 2.82 . (Same as Bonferroni example.) For Critical value: 50 . 2 * 12 , 3 ; 2 / 05 . 0 * , ; 2 / = = = ν = ν α p p tDN tDN • Compare to other critical values: Planned Orthogonal 2.179 Bonferroni 2.56 Sidak 2.52 (see Table E.7 in Kirk) Tukey’s HSD Test • Compares all possible pair-wise comparisons (case 4). • Assumes equal n across groups in Kirk. • Critical difference: n MS q qT error p ν α = ψ , ; ) ( ˆ (p. 145) is used to construct a 100(1- α )% confidence interval, . ) ( ˆ ˆ qT i ψ ± ψ ν α , ; p q is obtained by Table E.6.
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05_Mult Comp_3 - Dunn-Sidak Test - simply Sidak in SPSS A...

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