# ISS (Statistical Services) Statistics Paper IV: Questions 77 - 84 of 92

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## Question 77

Appeared in Year: *2014*

### Describe in Detail

Essay▾What do you understand by a split-plot design? When will such a design be adopted? Distinguish it from a usual confounded factorial experiment.

### 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. Split plot designs have a nested blocking structure i.e.. plots are nested within whole plots, which may be nested within blocks.

The Larger plots are call…

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## Question 78

Appeared in Year: *2014*

### Describe in Detail

Essay▾Define a Latin square design. Show how you split up the total sum of squares into components for this design. Give the analysis of variance table.

### Explanation

**Latin Square Design**:

When the experimental area is divided into rows and columns, and the treatments are allocated such a way that each treatments occurs only once in a row and once in a column, the design is called as Latin square design.

In LSD the number of rows and columns are equal and thus the arrangement will form a square. i.e.. in this desig…

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## Question 79

Appeared in Year: *2014*

### Describe in Detail

Essay▾Explain clearly the purposes of replications, randomizations and local control in design of experiments.

### Explanation

**Replication**:

Replication means the repetition of the basic experiments. In other words, the repetition of the treatments under investigation is known as Replication. The main purpose of the replication is to average out the influence of the chance factors on different experimental units.

The main advantages of Replication:

(i) It provides an estimate …

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## Question 80

### Explanation

If large number of treatments are to be compared, then large number of experimental units are required. This will increase the variation among the responses and CRD may not be appropriate to use. In such a case when the experimental material is not homogeneous and there are v treatments to be compared, then it may be possible to

- Group the experiment…

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## Question 81

### Describe in Detail

Essay▾Using the following data, perform a one way analysis of variance using . Write up the results in APA format.

### Explanation

Sample means for the groups:

Intermediate steps in calculating the group variances:

Sum of squared deviations from the mean (SS) for the groups:

Calculating the remaining error (or within) terms for the ANOVA table:

Intermediate steps in calculating the variance of the sample means:

Grand mean

…

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## Question 82

### Describe in Detail

Essay▾Using the following summary data, perform a one way analysis of variance using

### Explanation

Calculating the remaining error (or within) terms for the ANOVA table:

Intermediate steps in calculating the variance of the sample means:

Grand mean

Calculating the remaining between (or group) terms of the ANOVA table:

Test statistic and critical value

Decision: fail to reject H_{0}

**ANOVA table**:

Source | SS | df | MS |

Group | 1057.5 | 2 | 528.75 |

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## Question 83

### Explanation

**Experiments with two or more factors: (Two-way classification)** :

- We consider only the complete block design.
- Let there be
**J**treatments and**I**blocks. Consider the two way classification model where**J**different treatments are applied to each of**I**different blocks so that each block contains exactly**J**treatment and each treatment is replicated exactly**n**…

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## Question 84

### Describe in Detail

Essay▾Suppose different brands of petrol are to be compared with respect to the mileage per liter achieved in motor cars

Important factors responsible for the variation in the mileage are

• difference between individual cars.

• difference in the driving habits of drivers

### Explanation

- We have three factors – cars, drivers and petrol brands. Suppose we have types of cars denoted as 1,2, 3,4.
- 4 drivers that are represented by a, b, c, d.
- 4 brands of petrol are indicated by A, B, C, D.
- Now the complete replication will require number of experiments. We choose only 16 experiments. To choose such 16 experiments, we take the help of La…

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