Question

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3. In the two-way ANOVA cell means model Yijk = Hij + Eijk i = 1, ..., I j = 1,...,J a linear combination n is called an interaction contrast if k = 1, ..., hij n = Cij Mij > > i=lj=1 Gj = 0 for all j Cij = 0 for all i i.e., the constants Cij sum to zero over i for each j, and also over j, for each i.

Answer 1

wolucio" j,... J K2... Di Inleischio Yije - Mij + Eijk iz ljon ! lineas combination is called condmast y - g = F I CjMj [cij = 0 - Cj -o ti o assume [='3, J= 3 &j we have to dedeeone combination whethee it is an Coodrast fue each lineal interactos (2 rj, = Nil II = 1. I Cif Cliy = Ci su 2 - Nii => Cina | y is nod a indelados contrast 11) Je zull-la Ja - S & Cy =C NitCa Mia = Mil- Naa -G1=1 & (12=-1 I C = C11 +G2=1-1=0 32 is an interachos costas

m 43 = Willia - Nal + laa 1 ie 13 = 1 I ² Cij viji e Cu Mul + Ciawat CQ, Nait Cad Dad 2 2 = Nl-Nia - Na+ Naa =) C11=1 Cla=-1 Cal=-| Caa? . Ca =0 < C < 0 - H3 is as blenaction contrast IN Hg = (NI+Ua/ Warta/ 44 2 2 2 2 2 2 2 Cj Bij ci NL+ Cia Nia + Cal Nast Caa Naa % Nllt 1/2012 - Yaua 1/2022 -) C11 = 1/2 cia z / Cal=- Caaz-1/2 I gj: Ya+%231 to -1/2-²=-1 &O Jy is nod an interaction contrast.