Solution file for additional exercise 10.1
------------------------------------------

Dataset for additional exercise 10.2:
-------------------------------------
- notation:
y_ij = moisture content in j'th cheese in lot i,
   i = 1,2,3 (lot),
   j = 1,2 (cheese).
- the effect of lots should be taken as random if the purpose is
determination of the variability within the production (as it would seem
to be),
- model: 
y_ij = mu + A_i + eps_ij, where A_i's are assumed i.i.d. N(0,sigma_A^2) and
                          eps_ij's are assumed i.i.d. N(0,sigma^2).
- type of analysis: one-way ANOVA with random effects,
- ANOVA table:
Source	DF	F
----------------------------
Lots	2	MS(Lots)/MSE
Error	3
Total	5


Dataset for additional exercise 10.3:
-------------------------------------
- notation:
y_ijk = content measured in sample k of material j in laboratory i,
   i = 1,...,11 (lab),
   j = 1,2,3 (material),
   k = 1,2 (sample),
- the effect of labs should be taken as random because we have interest in
the variability between the laboratories (to compute the reproducibility),
- the effect of materials is fixed (the 3 concentrations are not chosen
at random, and do not represent any population),
- the interaction labs*material is random (because labs is random),
- model: 
y_ijk = mu + A_i + beta_j + (AB)_ij + eps_ijk, 
      where A_i's are assumed i.i.d. N(0,sigma_A^2),
      where AB_ij's are assumed i.i.d. N(0,sigma_AB^2), and
      where eps_ijk's are assumed i.i.d. N(0,sigma^2).
- type of analysis: two-way ANOVA with mixed effects (both fixed and random),
- ANOVA table:
Source		DF	F
----------------------------------------
Labs		10	MS(Labs)/MS(L*M)
Materials	2	MS(Mat)/MS(L*M)
Labs*Materials	20	MS(L*M)/MSE
Error		33
Total		65


Dataset for additional exercise 10.4:
-------------------------------------
- notation:
y_ijk = blood-pH value of k'th mouse in j'th litter of strain i,
   i = 1,2 (strain: pHH, pHL),
   j = 1,...,7 (litter, within strains),
   k = 1,2,3,4 (mouse),
- hierarchical structure in data: mice within litters (within strains),
- the factor litter may be considered nested within strain, because different litters
are used for the two strains (there is no link between litter no. 1 in
strain pHH and strain pHL),
- the effect of litter(strain) must be taken as random,
  * by the rule that hierarchical levels must be random effects,
  * in order to enable a comparison between strains (otherwise only 
    comparisons between litters is possible, if there is variation between litters),
- the effect of strain is fixed (we have specific interest in the 2 strains),
- model: 
y_ijk = mu + alpha_i + B_ij + eps_ijk, 
      where B_ij's are assumed i.i.d. N(0,sigma_B^2), and
      where eps_ijk's are assumed i.i.d. N(0,sigma^2).
- type of analysis: hierarchical model with two levels (mouse and litter),
- ANOVA table:
Source		DF	F
-------------------------------------------
Strains		1	MS(Strain)/MS(Litt)
Litters(Strain)	12	MS(Litt)/MSE
Error		42
Total		55