# ISS (Statistical Services) Statistics Paper IV: Questions 73 - 78 of 92

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## Question number: 73

» Design and Analysis of Experiments » Basic Principle of Experimental Design

Appeared in Year: 2010

### Describe in Detail

Show that for BIBD:

(i) bk = rv

(ii) r (k- 1) = (υ - l),

Further show that for resolvable BIBD:

b≥v + r-1 Name the design when equality holds good,

### Explanation

(i) In a BIBD **υ** treatments will be repeated **r** timesand hence total total number of plots in the design is **υr. **Further, there will be **b** blocks each of zize **k**, there will be **bk** plots all together.

hence** bk = rv**

** (ii) ** let us take be as the 1 x 1 matrix whose elements are unity.

(a) we know that

=

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## Question number: 74

» Design and Analysis of Experiments » Basic Principle of Experimental Design

Appeared in Year: 2013

### Describe in Detail

Discuss the concept of Balanced incomplete block design (BIBD). How does this design differ from randomized block design?

For a BIBD with parameters** , **b, r, kand** , **show that b** ≥ **

### Explanation

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 blocks and

(ii) Each pair of treatments occurs together in λ blocks.

The variance of the estimate of any treatment mean which has been replicated *r *times is where is the error variance. Thus in BIB

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## Question number: 75

» Design and Analysis of Experiments » Randomized Block and Latin Square Design

Appeared in Year: 2014

### Describe in Detail

Obtain necessary conditions for a symmetric BIBD with an even number of treatments to exist.

### Explanation

Necessary conditions for a symmetric BIBD with an even number of treatments to exist:

The determinant of is given by

=

Since

=

Using the fact

When BIBD is symmetric, r = k and b=

Substituting r = k and b=

We get,

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## Question number: 76

» Design and Analysis of Experiments » Need for Design of Experiments

Appeared in Year: 2014

### Describe in Detail

What is meant by the design of experiment? Describe the situations in which the three basic designs, namely CRD, RBD and LSD are appropriate, and state the rule or rules by which treatments are allocated to units in these designs.

### Explanation

**Design of experiment: **

Design of experiments may be defined a systematic method to determine the relationship between factors affecting a process and the output of that process.

The design of experiment includes:

(i) Planning of the experiment

(ii) Obtaining the relevant information from it regarding the statistical hypothesis under study

(ii

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## Question number: 77

» Design and Analysis of Experiments » Split Plot Design and Strip Plot Design

Appeared in Year: 2014

### Describe in Detail

What do you understand by a split-plot design? When will such a design be adopted? Distinguish it from a usual confounded factorial experiment.

### Explanation

**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. Split plot designs have a nested blocking structure i. e. plots are nested within whole plots, which may be nested within blocks.

The Larger plots are

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## Question number: 78

» Design and Analysis of Experiments » Randomized Block and Latin Square Design

Appeared in Year: 2014

### Describe in Detail

Define a Latin square design. Show how you split up the total sum of squares into components for this design. Give the analysis of variance table.

### Explanation

** Latin Square Design: **

When the experimental area is divided into rows and columns, and the treatments are allocated such a way that each treatments occurs only once in a row and once in a column, the design is called as Latin square design.

In LSD the number of rows and columns are equal and thus the arrangement will form a square. i. e. in thi

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