DESIGN OF EXPERIMENTS — DU B.Sc (hons) Statistics Previous Year Question Papers

3. Select four questions from the remaining six questions. (a) A student of Statistics has conducted a complete randomized design with different treatments to complete her experiment. The results of this experiment are summarized in the following ANOVA display: Source df Sum of Squares Mean squares Answer the following questions about this experiment: (i) The sum of squares for the treatment is _ (i) The number of degrees of freedom for treatments in the experiment is_ (iii) The number of degrees of freedom for error is (iv) The mean sum of squares due to error is _ (v) The value of the test statistic is - (b) Derive the expression to measure the efficiency of RBD over CRD, stating clearly the assumption used in the derivation. (c) An agricultural scientist wants to study the effect of three varieties of wheat Vi, V2, and V3 on crop yield. A field is divided into 12 plots. The varieties are assigned to the plots at the field is divided into four blocks of equal size. random, each variety being grown on four plots. Since soil fertility varies across the field, Answer the following questions about this experiment: (i) Name of the design and the number of treatments. (ii) Number of experimental units. (il) Number of replications. (iv) The principles of Design of Experiments used in this experiment. (d) Given a BIBD with parameters v = b = 7,r = k = 3,1 = 1. Obtain the dual of the given design along with the parameters. (e) Define a treatment contrast. When are two contrasts said to be orthogonal? Let Are these contrasts? If yes, which of them are orthogonal to each other? LA= [a- (1) +b-ab], Le = [(1)-a-bt ablandlc = [a+b-ab - (1)). (f) The key block in a 24 Factorial experiment is given as Identify all the confounded effects. Write down the contents of the remaining blocks. (g) Consider the following fractional factorial designs: What is the resolution of these designs? which design would you prefer and why? 2. (a) Discuss the three principles of the design of experiments. How are these principles used in a Latin Square design? (b) Describe the complete statistical analysis of an LSD to test the hypothesis of equality of all treatment effects. Also, write the complete ANOVA table. 3. (a) Prove that in an RBD, the mean sum of squares due to error is always an unbiased estimate of the error variance while the mean sum of squares due to treatments is a biased estimator. Under what condition is it unbiased? (b) Derive the least square estimates of the parameters in a randomized block design, clearly stating the model. Also, find the variance of the estimated parameters. 4. (a) Define resolvable and affine resolvable BIBDs. Also, prove that for a resolvable BIBD with parameters (v, b, r, k, 2); b ≥ 0+r- 1. (b) Define a Balanced Incomplete Block Design. Show that a BIBD with parameters (v, b,r, k, 1) satisfies the following relationships: 5. (a) Explain Yates technique for calculating sum of squares due to main effects and (6,9)