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formul sheet midterm

# formul sheet midterm - MSE-1 r-n q(r 2 1 Y-Y k i T k i α...

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SINGLE FACTOR FIXED MODEL I Y ij = jth observation on the ith factor level Y = Y ij n 1 = j i. i n Y = Y i . i . i n = n i r 1 = i T Y = Y ij n 1 = j r 1 = i . . i n Y = Y T .. .. μ μ τ . i i - = n n = T i i r 1 = i . μ μ n Y Y = SSTO T 2 .. 2 ij n j=1 r =1 i - i n Y - n Y = SSTR T 2 .. i 2 i. r =1 i 1 - r ) u. - ( n + = E{MSTR} 2 i i r 1 = i 2 μ σ Brown-Forsythe Test | M - Y | = d d ij ij i MSE MSTR = F * BR where n d d = SSTO T 2 .. 2 ij n j=1 r =1 i - i n d - n d = SSTR T 2 .. i 2 i. r =1 i Correlation Test Reject ε : H 0 are normally distributed if calculated correlation coefficient between the residuals and their expected value under normality is < tabulated value in B6 where z } e { E 0 ij for z 0 such that 1/4 + n 3/8 - k = ) z P(Z i 0 , if testing within each factor level Transformations : Y = Y : i 2 i μ σ (Y) = Y : i i log μ σ 1/Y = Y : 2 i i μ σ Linear combinations μ i i r =1 i c = L Y c = L i. i r =1 i ˆ n c = ) L ( Var i 2 i r =1 i 2 σ ˆ estimated n c MSE = ) L ( S = ) L Var( i 2 i r =1 i 2 ˆ ˆ Non-Parametric : 1) + n 3( - n R 1) + n ( n 12 = T i 2 i. r 1 = i T T 2 KW χ MSE MSTR = F * R where R ij = rank of jth observation of factor level i R i. = R ij n 1 = j i Simultaneous Estimation Procedures Tukey:
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Unformatted text preview: ( MSE )-1 r,-n q(r, 2 1 + Y-Y k i T k. i. α _ Scheffe: ∑ n c MSE F 1)-(r + L i 2 i r =1 i )-1 r,-n 1,-(r T _ ˆ Bonferroni: ∑ n c MSE t + L i 2 i 2g-1 r,-n T _ ˆ Response Curves and Lack of Fit Test Reject H: if F > MSPE MSLF = F-1 r,-n p,-r * T SSLF = SSTR - SSR = SSE(II) - SSE(I) SSE(I) = SSPE Regression Approach to ANOVA ij 1-r ij 1-r 2 ij 2 1 ij 1 . ij + X + ... + X + X + = Y n n = u T i i r 1 = i . ∑ b + b = + = Y i i . i. note that there should be “hats” on the mu. And tau...
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