# ISS (Statistical Services) Statistics Paper IV: Questions 65 - 71 of 92

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## Question 65

Appeared in Year: *2009*

### Describe in Detail

Essay▾Give the layout and analysis of a completely randomized design. Which of the basic principles are satisfied in this design and how?

### Explanation

**Layout of Completely Randomized Design (CRD)** : Here all the experimental units are taken in a single group that are homogeneous and randomization procedure for allotting the treatments to various units is as follows:

Step 1: Determine the total number of experimental units.

Step 2: Assign a plot number to each of the experimental units starting from …

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## Question 66

Appeared in Year: *2009*

### Describe in Detail

Essay▾What do you mean by confounding in a factorial experiment? Explain how you will obtain the confounded interactions from a key block.

### Explanation

**Confounding**: Confounding implies thatdevice of reducing the block size by making one or more interaction contrasts identical with block contrasts is taken. It is technique to decrease size of a replication over a number of blocks at the cost of losing some information on some effect which is not of much practical importance.

The device of confoundin…

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## Question 67

Appeared in Year: *2013*

### Describe in Detail

Essay▾Explain split-plot designs. Considering main plot treatment α , sub-plot treatment β and the number of replications in the RBD for main plot treatments be r, write the ANOVA table of main plot totals.

### Explanation

**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.

The smaller plots wit…

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## Question 68

Appeared in Year: *2009*

### Write in Brief

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

## Question 69

Appeared in Year: *2009*

### Describe in Detail

Essay▾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 subplots or …

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## Question 70

Appeared in Year: *2011*

### Describe in Detail

Essay▾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 if and onlu if ith and lth treatments occur together in the jth block otherwise it is 0 and they occur together in

If N՚ denotes the t…

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## Question 71

Appeared in Year: *2010*

### Describe in Detail

Essay▾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 direction…

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