# Design and Analysis of Experiments (ISS (Statistical Services) Statistics Paper IV): Questions 1 - 7 of 48

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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) are called the parameters of

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## Question number: 2

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

Appeared in Year: 2012

### Describe in Detail

Discus symmetrical BIBD. For an SBIBD, under usual notations, show that

=

### 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

**Proof:** **=**

Let N be the

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## Question number: 3

» 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: 4

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

Appeared in Year: 2011

### Write in Short

Explain Randomized block design.

## Question number: 5

» 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 carried out

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## Question number: 6

» Design and Analysis of Experiments » Analysis of Variance for 1 Way and 2 Way Classifications

Appeared in Year: 2012

### Describe in Detail

What is a factorial experiment? Discuss a method to estimate all main effects and interaction effects considering replication size *r.* Also, write its ANOVA table.

### Explanation

**Factorial experiment:**

The factorial experiment is a two level factorial experiment design with three factors. Let us consider A, B, C as the three factors under study. Then This design tests three main effects (A, B and C) and three, two factorial effects (AB, BC, AC) and one factor interaction effect (ABC). There will be eight treatment c

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## Question number: 7

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

Appeared in Year: 2010

### Describe in Detail

Discuss the layout for 2^{3} factorial experiment with suitable illustration, how would you carry out the analysis of such a design?

### Explanation

Here we will have 3 factors each at two levels. Let A, B, C be three factors under study and let small letters a, b, and c represent the two levels of each of the corresponding factors. say,

( ), there will be treatment combinations in all.

The 8 treatment combinations will be

1, a, b, ab, c, ac, b

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