# Design and Analysis of Experiments (ISS (Statistical Services) Statistics Paper IV): Questions 14 - 19 of 36

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## Question number: 14

» Design and Analysis of Experiments » Analysis and Layout of Completely Randomized Design

Appeared in Year: 2012

### Describe in Detail

Let four treatments be arranged in three blocks. The arrangement is given below:

Block 1:

Block 2:

Block 3:

Identify the block design. Write its parameters. If the treatment in Block 3 is missing, estimate the missing value. Write its ANOVA table.

### Explanation

This is the Randomized block design. (RBD)

its parameters are t = treatments 4 and Blocks r = blocks = 3

Here i = 1, 2, 3, 4 and j = 1, 2, 3

Let the missing value be in Block 3.

## Question number: 15

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

Appeared in Year: 2010

### Describe in Detail

What is confounding in a factorial experiment? Explain why it is necessary. Enumerate the advantages and disadvantages for confounding.

### Explanation

The process by which unimportant comparisons are mixed up with the block comparisons, for assessing more important comparisons with greater precision is called confounding. It is also defined as the technique of reducing the size of a replication over a number of blocks at the cost of losing some information

## Question number: 16

» 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

## Question number: 17

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

Appeared in Year: 2013

### 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

## Question number: 18

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

Appeared in Year: 2013

### 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

## Question number: 19

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

Appeared in Year: 2011

### 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