# Design and Analysis of Experiments (ISS (Statistical Services) Statistics Paper IV): Questions 27 - 32 of 36

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## Question number: 27

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

Appeared in Year: 2011

### Describe in Detail

For symmetric BIBD, show that , where N is the incidence matrix of SBIBD.

### Explanation

Let N= be the incident matrix of a SBIBD with parameters υ, b, k, r, λ. denotes the number of times the ith treatment occurs in the jth block then by Definition of BIBD

Where

, otherwise

By definition of BIBD

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## Question number: 28

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

Appeared in Year: 2010

### Describe in Detail

Describe under which situations a Latin square design can be preferred to completely randomised design and randomised block design, What are the merits and demerits of LSD?

### Explanation

(i) **Latin square design compared to completely Randomized design: **

In CRD, we allocate the treatments at random to the experimental units, without the grouping of the experimental field. In some cases, this design suffers because of not having more information like other advanced designs. Since in CRD randomisation is not restricted in any direct

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## Question number: 29

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

Appeared in Year: 2012

### Describe in Detail

Discuss the layout of a Latin square design. Give its example. Write its model (one observation per experimental unit). Give its ANOVA table. Write null hypothesis. Give comments on acceptance and rejection of null hypothesis**. **

### Explanation

**Layout of Latin Square designs: **

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.

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## Question number: 30

» 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: 31

» 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: 32

» 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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