# ISS (Statistical Services) Statistics Paper IV: Questions 68 - 74 of 79

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## Question number: 68

» 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: 69

» Design and Analysis of Experiments » Split Plot Design and Strip Plot Design

Appeared in Year: 2009

### Describe in Detail

What is a split plot design? Give an example of a situation where this is a natural choice. Outline the analysis of data from a split-plot experiment where the main plots form the randomized block.

### Explanation

**Plot Design: **

A split plot design is a design with at least one blocking factor where the experimental units within each block are assigned to the treatment factor levels and also blocks are assigned at random to the levels of a further treatment factor. So there are two levels of

## Question number: 70

» 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

, otherwise

By definition of BIBD

since

## Question number: 71

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

Appeared in Year: 2010

### Describe in Detail

Describe under which situations a Latin square design can be preferred to completely randomised design and randomised block design, What are the merits and demerits of LSD?

### Explanation

(i) **Latin square design compared to completely Randomized design: **

In CRD, we allocate the treatments at random to the experimental units, without the grouping of the experimental field. In some cases, this design suffers because of not having more information like other advanced designs. Since in CRD randomisation is not

## Question number: 72

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

Appeared in Year: 2012

### Describe in Detail

Discuss the layout of a Latin square design. Give its example. Write its model (one observation per experimental unit). Give its ANOVA table. Write null hypothesis. Give comments on acceptance and rejection of null hypothesis**. **

### Explanation

**Layout of Latin Square designs: **

When the experimental area is divided into rows and columns, and the treatments are allocated such a way that each treatments occurs only once in a row and once in a column, the design is called as Latin square design.

In LSD the number of

## Question number: 73

» 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: 74

» 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