# ISS (Statistical Services) Statistics Paper IV: Questions 59 - 64 of 92

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## Question number: 59

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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 in r

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## Question number: 60

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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, If is the

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## Question number: 61

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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 Agric

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## Question number: 62

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Discuss symmetrical BIBD. For a SBIBD, show that any two blocks have exactly λ treatments in common.

### Explanation

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

For a SBIBD, any two blocks have exactly λ treatments in common.

To pr

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## Question number: 63

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Explain the layout of split plot designs. Write its model and assumptions. Give ANOVA table of sub-plot observations· (only df and sum of squares).

### Explanation

Layout of split plot designs:

The split plot is a design which involves assigning the levels of one factor to large plots and then assigning the levels of a second factor to subplots within each main plot.

The Larger plots are called main plots or whole plots and The factor levels allotted to the main plots are called main plot treatments.

The smaller

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## Question number: 64

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Appeared in Year: 2009

Essay Question▾

### Describe in Detail

Obtain an estimate of a missing observation in a Latin square design. How does the subsequent analysis differ from the usual case?

### Explanation

Let us suppose that in Latin square, the observation occurring in the ith row and jth column and receiving the kth treatment is missing.

Let us assume that its value is x, i. e. = .

= total of the known observations in the ith row, i. e. the row containing

= total of known observations in the jth column, i. e. the column co

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