# ISS (Statistical Services) Statistics Paper IV: Questions 61 - 67 of 79

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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

## 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

## 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

## 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

## 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

## 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

## 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