# Design and Analysis of Experiments-Randomized Block and Latin Square Design (ISS (Statistical Services) Statistics Paper IV): Questions 8 - 10 of 10

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## Question number: 8

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

Appeared in Year: 2012

Essay Question▾

### 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.…

… (337 more words) …

## Question number: 9

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

Appeared in Year: 2014

Essay Question▾

### 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,

since

=

=

Since the determinant of the incidence matrix, i. e. , is an integer, hence when is even, must be a perfect sq…

… (14 more words) …

## Question number: 10

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

Appeared in Year: 2014

Essay Question▾

### 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…

… (258 more words) …

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