# ISS (Statistical Services) Statistics Paper IV: Questions 61 - 67 of 92

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## Question number: 61

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

Appeared in Year: 2013

### Describe in Detail

Explain the need of Factorial experiments. Develop a method to estimate all main effects and interaction effects of ** **-factorial experiment. Give its ANOVA table.

### Explanation

**Need of Factorial experiments: **

A factorial design is used to understand the effect of two or more independent variables upon a single dependent variable. Several factors affect simultaneously the characteristic under study. Factorial experiments helps to study the main effects and the interaction effects among different factors.

For example, in

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## Question number: 62

» Design and Analysis of Experiments » Basic Principle of Experimental Design

Appeared in Year: 2011

### Describe in Detail

Discuss symmetrical BIBD. For a SBIBD, show that any two blocks have exactly λ treatments in common.

### Explanation

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

For a SBIBD, any two blocks have exactly λ treatments in

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## Question number: 63

» Design and Analysis of Experiments » Basic Principle of Experimental Design

Appeared in Year: 2011

### Describe in Detail

Explain the layout of split plot designs. Write its model and assumptions. Give ANOVA table of sub-plot observations· (only df and sum of squares).

### Explanation

Layout of 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.

Th

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## Question number: 64

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

Appeared in Year: 2009

### Describe in Detail

Obtain an estimate of a missing observation in a Latin square design. How does the subsequent analysis differ from the usual case?

### Explanation

Let us suppose that in Latin square, the observation occurring in the i^{th} row and j^{th} column and receiving the k^{th} treatment is missing.

Let us assume that its value is x, i. e. = .

= total of the known observations in the i^{th} row, i. e. the row containing

= total of known observ

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## Question number: 65

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

Appeared in Year: 2009

### Describe in Detail

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 f

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## Question number: 66

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

Appeared in Year: 2009

### Describe in Detail

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 confoun

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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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