S Two factor ANOVA, or two way layout, with one observation per cell Consider the situation of Example (12 34) for the case that D 1 Then V wg D 0, and the results from (12 34) are no longer applicable Therefore, this experimental design only makes sense when it is a priori clear that the factors do not interact, so that the additive two factor model Xij D C i C j C p v ij ij 2 G applies here i j are unknown parameters that satisfy P i2G1 i D 0 and P j2G2 j D 0 Characterise the linear space L of all vectors of the form Ci Cj ij2G by a system of equations, determine the projection of the observation vector X onto L, and design an F test of the null hypothesis H0 W factor 1 has no influence

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Question: S Two-factor ANOVA, or two-way layout, with one observation per cell. Consider the situation of Example (12.34) for the case that ` D 1. Then

S Two-factor ANOVA, or two-way layout, with one observation per cell. Consider the situation of Example (12.34) for the case that ` D 1. Then V

wg D 0, and the results from

(12.34) are no longer applicable. Therefore, this experimental design only makes sense when it is a priori clear that the factors do not interact, so that the ‘additive two-factor model’

Xij D C ˛i C ˇj C p

v ij; ij 2 G;

applies; here ; ˛i; ˇj are unknown parameters that satisfy P

i2G1

˛i D 0 and P

j2G2

ˇj D 0. Characterise the linear space L of all vectors of the form .C˛i Cˇj /ij2G by a system of equations, determine the projection of the observation vector X onto L, and design an F -test of the null hypothesis H0 W ‘factor 1 has no influence’.

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