# ISS (Statistical Services) Statistics Paper IV: Questions 49 - 54 of 92

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## Question number: 49

» Design and Analysis of Experiments » Analysis of Variance for 1 Way and 2 Way Classifications

Appeared in Year: 2012

### Describe in Detail

What is a factorial experiment? Discuss a method to estimate all main effects and interaction effects considering replication size *r. * Also, write its ANOVA table.

### Explanation

**Factorial experiment: **

The factorial experiment is a two level factorial experiment design with three factors. Let us consider A, B, C as the three factors under study. Then This design tests three main effects (A, B and C) and three, two factorial effects (AB, BC, AC) and one factor interaction effect (ABC). There will be ei

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## Question number: 50

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

Appeared in Year: 2010

### Describe in Detail

Discuss the layout for 2^{3} factorial experiment with suitable illustration, how would you carry out the analysis of such a design?

### Explanation

Here we will have 3 factors each at two levels. Let A, B, C be three factors under study and let small letters a, b, and c represent the two levels of each of the corresponding factors. say,

(), there will be treatment combinations in all.

The 8

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## Question number: 51

» Design and Analysis of Experiments » Analysis of Covariance

Appeared in Year: 2009

### Describe in Detail

What is the use of analysis of covariance? Give the general procedure of analysis of covariance for a RBD, stating the necessary assumptions.

### Explanation

**Analysis of Covariance (ANCOVA) **: Extension of ANOVA gives way of statistically controlling the (linear) effect of variables one does not want to examine and the extraneous variables are called covariates, or control Variables. It allows removing covariates from the list of possible explanations of variance in the dependent variable.

**ANCOVA is us**

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## Question number: 52

» Design and Analysis of Experiments » Analysis of Covariance

Appeared in Year: 2010

### Describe in Detail

Discuss the procedure for carrying out the analysis and testing procedure by means of ANOVA table for two-way classification.

### Explanation

Two-way ANOVA technique is used when there are two factors, which may affect the variate values. For example, the agricultural output may be affected by difference in treatments on the basis of seeds and also on the different fertilizers used.

Let there be two factors A and B which affect the variate value. Let X_{ijk} (i = 1,2, . . p; j = 1,2, …, q

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## Question number: 53

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

Appeared in Year: 2010

### Describe in Detail

Treatments N, P, K and S are administered in 4 blocks through 4 columns. The layout of design is as shown below:

Columns

N | P | K | S |

P | K | S | N |

K | S | N | P* |

S | N | P | K |

Blocks

Identify the above design. If the observation (*) in third row and fourth column is missing, how would you estimate the missing yield?

### Explanation

This is a 4 x 4 Latin square design with one missing observation.

**Estimation of the missing yield: **

The observation in the (i^{th}) 3^{rd} row, (j^{th}) 4^{th} column is missing.

i. e.

m = number of rows or columns in the design (here 4 x 4. hence m = 4)

R = Sum of the known observations in the 3^{rd} row, i

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## Question number: 54

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

Appeared in Year: 2013

### Describe in Detail

Identify the design given below, whose blocks are:

(1,2, 3,4); (2,3, 4,1) and (4,1, 2,3).

Write its parameters. Suppose a treatment ‘3’ belonging to 3^{rd} row and 4^{th} column is missing. How can you estimate that missing treatment? Estimate that value. Write degrees of freedom for error and total variation.

### Explanation

This is the Randomized block design. (RBD)

Its parameters are t = treatments 4 and Blocks r = blocks = 3

Here i = 1,2, 3,4 and j = 1,2, 3

**The method of estimating the missing value: **

let us consider the missing value as belonging to 3^{rd} row and 4^{th} column

Treatment | |||||

Blocks | 1 | 2 | 3 | 4 | Total |

1 | |||||

2 | |||||

3 | |||||

Total |

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