# Design and Analysis of Experiments-Randomized Block and Latin Square Design [ISS (Statistical Services) Statistics Paper IV]: Questions 1 - 6 of 12

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## Question number: 1

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

Appeared in Year: 2015

### Describe in Detail

Discuss how you would proceed with the analysis if data on one plot is missing in a Latin Square design.

### Explanation

To analysis the data of a Latin square design having missing values, we first estimate the missing value by minimizing the error mean square and the rest missing values by guess estimate which is generally the mean of all available values. The estimated value of x is obtain by to minimize the error variance, differentiate the expression for it with

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## Question number: 2

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

Appeared in Year: 2010

### Describe in Detail

Treatments N, P, K and S are administered in 4 blocks through 4 columns. The layout of design is as shown below:

Columns

N | P | K | S |

P | K | S | N |

K | S | N | P* |

S | N | P | K |

Blocks

Identify the above design. If the observation (*) in third row and fourth column is missing, how would you estimate the missing yield?

### Explanation

This is a 4 x 4 Latin square design with one missing observation.

**Estimation of the missing yield:**

The observation in the (i^{th}) 3^{rd} row, (j^{th}) 4^{th} column is missing.

i. e.

m = number of rows or columns in the design (here 4 x 4. hence m = 4)

R = Sum of the known observations in the 3^{rd} row, i. e. the row containing P

C =

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## Question number: 3

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

Appeared in Year: 2010

### 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: 4

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

Appeared in Year: 2009

### 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 i^{th} row and j^{th} column and receiving the k^{th} treatment is missing.

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

= total of the known observations in the i^{th} row, i. e. the row containing

= total of known observations in the j^{th} column, i. e. the column co

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## Question number: 5

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

Appeared in Year: 2009

### Write in Brief

Explain the term ‘connected’ in the context of block designs.

## Question number: 6

» 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

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