# 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 occur together in blocks (i = 1,2, . . , m)

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## 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 of Replication: __ The experiment has to be carri

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## 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 = block size

λ=number of blocks in which any pair of treatments occurs together

**To obtain the ****relation between N and ****λ****, ****I**

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## 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 size

λ=number of blocks in which any pair of treatments occurs together

For a SBIBD, any two blocks have exactly λ treatments in

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## 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 levels allotted to the main plots are called main plot treatments.

Th

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## 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 as the 1 x 1 matrix whose elements are unity.

(a) we know that

=

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## 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 treatment mean which has been replicated *r *times is where is the er

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