# ISS (Statistical Services) Statistics Paper IV: Questions 55 - 61 of 79

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## Question number: 55

Appeared in Year: 2009

Essay Question▾

### 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

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## Question number: 56

Appeared in Year: 2011

Essay Question▾

### 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 co

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## Question number: 57

Appeared in Year: 2012

Essay Question▾

### 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. ‎

 Treatment Blocks 1 2 3 4 Total 1 2 3 Total

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## Question number: 58

Appeared in Year: 2010

Essay Question▾

### Describe in Detail

What is confounding in a factorial experiment? Explain why it is necessary. Enumerate the advantages and disadvantages for confounding.

### Explanation

The process by which unimportant comparisons are mixed up with the block comparisons, for assessing more important comparisons with greater precision is called confounding. It is also defined as the technique of reducing the size of a replication over a number of blocks at the cost of losing some information on some effect, which is not of much pr

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## Question number: 59

Appeared in Year: 2010

Essay Question▾

### Describe in Detail

Define SBIBD. Show that for SBIBD, if the number of treatments is even then (r- λ) is a perfect square.

### Explanation

Block design in combinatorial mathematics is a set with family of subsets (repeated subsets are allowed at times) whose members are picked to satisfy set of properties deemed useful for a particular application.

An arrangement of the υ treatments in b blocks of k plots each (k < υ) is known as BIBD if

(i) Each treatment occurs once and only once

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## Question number: 60

Appeared in Year: 2013

Essay Question▾

### Describe in Detail

What is a symmetrical BIBD? If N is the incidence matrix of SBIBD and is the number of treatments common in any two blocks, then establish a relation between N and λ.

### 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

To obtain the relation between N and λ,

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## Question number: 61

Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Explain the need of Factorial experiments. Develop a method to estimate all main effects and interaction effects of -factorial experiment. Give its ANOVA table.

### Explanation

Need of Factorial experiments:

A factorial design is used to understand the effect of two or more independent variables upon a single dependent variable. Several factors affect simultaneously the characteristic under study. Factorial experiments helps to study the main effects and the interaction effects among different factors.

For example, in

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