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

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Appeared in Year: 2012

Essay Question▾

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

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Appeared in Year: 2010

Essay Question▾

Describe in Detail

Discuss the layout for 23 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

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Appeared in Year: 2009

Essay Question▾

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

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Appeared in Year: 2010

Essay Question▾

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 Xijk (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

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Appeared in Year: 2010

Essay Question▾

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

Design and Analysis of Experiments

Latin Square Designs

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 (ith) 3rd row, (jth) 4th 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 3rd row, i

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Question number: 54

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

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Appeared in Year: 2013

Essay Question▾

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 3rd row and 4th 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 3rd row and 4th column‎

How to find the missing value

Method to estimate the missing value

Treatment

Blocks

1

2

3

4

Total

1

2

3

Total

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