# ISS (Statistical Services) Statistics Paper IV: Questions 47 - 53 of 92

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## Question 47

## Question 48

Appeared in Year: *2015*

### Describe in Detail

Essay▾Explain briefly the main principles of design of experiment and analogy in sample surveys with the corresponding concepts.

### Explanation

The main principle of design of experiment is to study the sampling error. If these principles hold, the chance of getting a data set or a design which could be analyzed, with less doubt about structural nuisances, is higher as if the data was collected arbitrarily.

__Principle 1: Fisher՚s Principle of Replication__: The experiment has to be carried out…

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## Question 49

Appeared in Year: *2012*

### Describe in Detail

Essay▾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 eight treatment combinati…

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## Question 50

Appeared in Year: *2010*

### Describe in Detail

Essay▾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 treatment combinations will be

1, a, b, ab, c, ac, bc, abc where 1 = , etc.

These 8 treatment combinati…

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## Question 51

Appeared in Year: *2009*

### Describe in Detail

Essay▾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 used …**

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## Question 52

Appeared in Year: *2010*

### Describe in Detail

Essay▾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 53

Appeared in Year: *2010*

### Describe in Detail

Essay▾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 × 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 × 4 . hence m = 4)

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

C = Sum of known observations in th…

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