For each of the following data sets, concisely describe the design of the experiment (including the treatment design) and provide a model equation similar in format to those on the handout "Model Equations for Some Basic Experimental Designs". For most (perhaps all) of the experiments, you can refer to an equation number, but define specifically what is represented by the model equation components. In each

case choose a model that would make it possible to estimate experimental error variance. Write out the Source and Degrees of Freedom columns for all experiments, including a row for the Total and its associated df.

(a)P. 62-63, Problem 3.3.

(b)P. 200, Problem 8.4.

(c)P. 200-201, Problem 8.5.

(d)P. 201, Problem 8.6.

(e)P. 202, Problem 8.7.

(f)P. 346, Exercise 13.2.

(g)P. 350-351, Problem 13.7.

LINK FOR PROBLEM DATASETS: http://users.stat.umn.edu/~gary/book/hwprobs.dat.txt

Model Equations for Some Basic Experimental Designs (1) CRD with one treatment factor (t treatments, treatment i has sample size n;): Y =utt + 8 ;i=1,...,t; j = 1,...,n; (2) RCBD with one treatment factor (r blocks, t treatments): Y = u+p, +t, + 8;i=1,....r; j=1,...,t (3) CRD with two treatment factors (axb factorial, n (= r) > 1 experimental unit per treatment): Yu = H+ a, + B, + (aB), + ;i=1,...,a; j = 1,...,b;k = 1, ...,n (4) CRD with two treatment factors (axb factorial, n = experimental unit per treatment, assume no AB interaction): Y = +a, + B, + & ;i =1,...,a; j =1,...,b(5) RCBD with two treatment factors (axb factorial, r blocks): Yak = U+ p; + a; + B,+ (aB), + Ex; i=1,...,1; j =1,...,a; k = 1,...,b (6) CRD with three treatment factors (axbxc factorial, n (=r) experimental units per treatment): YUH = 1 + a, + B, + 7x + (ap), + (ay) + (BY), + (aBy ) , + ETH; i =1,...,a; j =1,..,b;k =1,...,c;/ =1,..., n (7) CRD with three treatment factors (axbxc factorial, one experimental unit per treatment, assume no ABC interaction): Yx = u + a; + B, + yx + (ap); +(ap) + ( BY), + Eqx; i = 1,...,a; j =1,...,b; k =1, ...,c (8) RCBD with three treatment factors (axbxc factorial, r blocks): YUH = u + P, + a, + Bx + 1, + ( ap), + (ap), + (BY) H + (aBy) ,H + EGH; i = 1,...,1; j =1,..,a; k = 1, ...,b;/ =1,....c