# Design and Analysis of Experiments-Basic Principle of Experimental Design (ISS (Statistical Services) Statistics Paper IV): Questions 1 - 7 of 8

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## Question number: 1

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

Appeared in Year: 2013

### Describe in Detail

For a PBIB design with parameters**, **b, r, k**, ****, **show that

### Explanation

A PBIB design with m associate classes based on the association scheme is an arrangement of treatments into b blocks such that

(i) Each block contains k distinct treatments (k <

(ii) Each treatment occurs in r blocks

(iii) Any two treatments, which are ith associates

## Question number: 2

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

Appeared in Year: 2015

### Describe in Detail

Explain briefly the main principles of design of experiment and analogy in sample surveys with the corresponding concepts.

### Explanation

The main principle of design of experiment is to study the sampling error. If these principles hold, the chance of getting a data set or a design which could be analyzed, with less doubt about structural nuisances, is higher as if the data was collected arbitrarily.

__Principle 1: Fisher’s Principle__

## Question number: 3

» 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: 4

» 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

## Question number: 5

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

Appeared in Year: 2011

### Describe in Detail

Explain the layout of split plot designs. Write its model and assumptions. Give ANOVA table of sub-plot observations· (only df and sum of squares).

### Explanation

Layout of 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.

The Larger plots are called main plots or whole plots and The factor

## Question number: 6

» 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

## Question number: 7

» 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