# ISS (Statistical Services) Statistics Paper IV: Questions 68 - 73 of 92

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## Question number: 68

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Appeared in Year: 2009

One Liner Question▾

### Write in Brief

Explain the term ‘connected’ in the context of block designs.

## Question number: 69

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Appeared in Year: 2009

Essay Question▾

### 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 experimental units.

Whole plots is the name for blocks and subplo

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## Question number: 70

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Appeared in Year: 2011

Essay Question▾

### 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

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## Question number: 71

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Appeared in Year: 2010

Essay Question▾

### 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 restricted in any direct

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## Question number: 72

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Appeared in Year: 2012

Essay Question▾

### 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 rows and columns are equal and thus the arrangement will form a square. i.

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## Question number: 73

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Appeared in Year: 2010

Essay Question▾

### 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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