# Design and Analysis of Experiments-Analysis and Layout of Completely Randomized Design [ISS (Statistical Services) Statistics Paper IV]: Questions 1 - 6 of 8

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## Question number: 1

» Design and Analysis of Experiments » Analysis and Layout of Completely Randomized Design

Appeared in Year: 2012

### Describe in Detail

Discus symmetrical BIBD. For an SBIBD, under usual notations, show that

=

### Explanation

**Symmetrical BIBD**:

A BIBD is said to be symmetric if b= υ and r = k.

υ, r, b, k and λ are called the parameters of the BIBD

υ= number of varities or treatments

b = number of blocks

r = number of replicates for each treatment

k = block size

λ=number of blocks in which any pair of treatments occurs together

**Proof:** **=**

Let N be the

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## Question number: 2

» Design and Analysis of Experiments » Analysis and Layout of Completely Randomized Design

Appeared in Year: 2011

### Write in Short

Explain Randomized block design.

## Question number: 3

» Design and Analysis of Experiments » Analysis and Layout of Completely Randomized Design

Appeared in Year: 2013

### Describe in Detail

Identify the design given below, whose blocks are:

(1,2, 3,4); (2,3, 4,1) and (4,1, 2,3).

Write its parameters. Suppose a treatment ‘3’ belonging to 3^{rd} row and 4^{th} column is missing. How can you estimate that missing treatment? Estimate that value. Write degrees of freedom for error and total variation.

### Explanation

This is the Randomized block design. (RBD)

Its parameters are t = treatments 4 and Blocks r = blocks = 3

Here i = 1,2, 3,4 and j = 1,2, 3

**The method of estimating the missing value:**

let us consider the missing value as belonging to 3^{rd} row and 4^{th} column

is the total of all available (r-1) observations for i^{th} treatment

is the total

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## Question number: 4

» Design and Analysis of Experiments » Analysis and Layout of Completely Randomized Design

Appeared in Year: 2009

### Describe in Detail

Explain the uniformity trials. Discuss their role in picking up a proper design.

### Explanation

Uniformity trials helps to give idea about the fertility variation of the field.

A trial in which the field (experimental material) is divided into small units (plots) and the same treatment is applied on each of the units and their fields are recorded. From these yields, ‘fertility counter map’ is made for graphic picture of the variation of the so

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## Question number: 5

» Design and Analysis of Experiments » Analysis and Layout of Completely Randomized Design

Appeared in Year: 2011

### Describe in Detail

Discuss missing plot techniques in a RBD. Suppose one observation, say, is missing in one block of a RBD, derive a method to estimate that missing value.

### Explanation

Missing plot techniques in a RBD:

Sometimes observations from one or more experimental units will be missing due to some unavoidable causes. There might be many unforeseen causes, for example, in agricultural experiments damages by pets or in animal experiment any animal may die or the observations from one or more plot is excessively large as compa

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## Question number: 6

» Design and Analysis of Experiments » Analysis and Layout of Completely Randomized Design

Appeared in Year: 2012

### Describe in Detail

Let four treatments be arranged in three blocks. The arrangement is given below:

Block 1:

Block 2:

Block 3:

Identify the block design. Write its parameters. If the treatment in Block 3 is missing, estimate the missing value. Write its ANOVA table.

### Explanation

This is the Randomized block design. (RBD)

its parameters are t = treatments 4 and Blocks r = blocks = 3

Here i = 1,2, 3,4 and j = 1,2, 3

Let the missing value be in Block 3.

is the total of all available (r-1) observations for i^{th} treatment

is the total of all available (t-1) observations in j^{th} block

is the total o

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