# ISS (Statistical Services) Statistics Paper IV: Questions 67 - 72 of 79

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## Question number: 67

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

Appeared in Year: 2013

### Describe in Detail

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 pl

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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 experimental units.

Whole plots is the name for blocks and subplo

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## 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

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## 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 restricted in any direct

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

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