Below is given the plan and yields of 22 -Factorial Experiment involving 2 factors A and B each at two levels 0 and 1. Analyse the design
| Block I | |||
| 117 (1) | 106 b | 129 ab | 124 a |
| Block II | |||
| 124 ab | 120 (1) | 117 b | 124 a |
| Block III | |||
| 111 (1) | 127 a | 114 b | 126 ab |
| Block IV | |||
| 125 ab | 131 a | 112 b | 108 (1) |
| Block V | |||
| 95 ab | 97 b | 73 (1) | 128 a |
| Block VI | |||
| 158 a | 81 (1) | 125 ab | 117 b |
Does treatment effect A differs from treatment effect B?
We are asked to analyze a $2^2$ factorial experiment with two factors $A$ and $B$ at two levels (0 and 1), given the yields in six blocks. Let’s solve this manually. --- Step 1: Identify the treatment combinations. For $2^2$ factorial: | Factor A | Factor B | Treatment | | -------- | -------- | --------- | | 0 | 0 | 1 | | 1 | 0 | a | | 0 | 1 | b | | 1 | 1 | ab | --- Step 2: Compute average yield for each treatment across all blocks. We collect the yields for each treatment: * Treatment 1 (A0B0): ________ __________ ______ _________ ______ __________ ________ _____ _____ ________.
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Explain what is meant by a one-quarter fractional factorial experiment of a 2 2 factorial experiment. Give a notation which denotes the one-quarter fractional factorial design.
Define the difference estimator for the population mean. Show that it is an unbiased estimator and its variance is given by where symbols have their usual meanings.
Define the Residual B.I.B.D. and Derived B.I.B.D. of a given symmetric B.I.B.D. Mention the rule of constructing a residual B.I.B.D. corresponding to a specific B.I.B.D.
then (X, ) is a (5, 3, 3)- B.I.B.D. Find the incidence matrix of this B.I.B.D.
Let us consider the following Balanced Incomplete Block Design (B.I.B.D.) with parameters
| Block Label | Design |
| I | 1 3 4 5 |
| II | 1 4 6 7 |
| III | 1 2 5 7 |
| IV | 3 5 6 7 |
| V | 2 3 4 7 |
| VI | 1 2 3 6 |
| VII | 2 4 5 6 |
State whether the following statements are true or false and also give the reason in support of your answer:
a) If X and Y are uncorrelated, the V(Rag) reduces to that of Variance of Ratio Estimator of Population mean
b) Among all the members of the General Class of the estimators only Regression estimator is an unbiased estimator of the Population mean.
c) An Incomplete Block Design with the following parameters b=8,k=3,9=8,r=3 is found to be a Balanced Incomplete Block Design.
d) A One-half fractional factorial design of a 2ª full factorial design will be denoted by a 22 Factorial design.
e) The Cluster estimator ỹ, becomes an unbiased estimator of population mean only if M and , are uncorrelated
Below is given the plan and yields of 22 -Factorial Experiment involving 2 factors A and B each at two levels 0 and 1. Analyse the design
| Block I | |||
| 117 (1) | 106 b | 129 ab | 124 a |
| Block II | |||
| 124 ab | 120 (1) | 117 b | 124 a |
| Block III | |||
| 111 (1) | 127 a | 114 b | 126 ab |
| Block IV | |||
| 125 ab | 131 a | 112 b | 108 (1) |
| Block V | |||
| 95 ab | 97 b | 73 (1) | 128 a |
| Block VI | |||
| 158 a | 81 (1) | 125 ab | 117 b |
Suppose we wish to estimate the total number of Cows in 2026 in certain state. The total number of cows for 2024 was X = 5000. The Sampling unit was the farm, and it is assumed that there has been no change in the number of farms which we shall assume to be N=500. A sample of n=20 farms is selected, and the data is as follows:
| Farm | 2024 | 2026 | Farm | 2024 | 2026 |
| 1 | 12 | 14 | 11 | 11 | 14 |
| 2 | 22 | 25 | 12 | 17 | 19 |
| 3 | 38 | 37 | 13 | 12 | 12 |
| 4 | 15 | 18 | 14 | 22 | 23 |
| 5 | 18 | 20 | 15 | 14 | 16 |
| 6 | 31 | 30 | 16 | 26 | 28 |
| 7 | 15 | 15 | 17 | 08 | 09 |
| 8 | 20 | 21 | 18 | 16 | 15 |
| 9 | 10 | 12 | 19 | 13 | 15 |
| 10 | 25 | 12 | 20 | 19 | 20 |