# ISS (Statistical Services) Statistics Paper IV: Questions 83 - 90 of 92

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## Question number: 83

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

### Describe in Detail

Explain Design of Experiments for Two-way classification.

### 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 number: 84

» Design and Analysis of Experiments » Factorial and Confounding in 2 and 3a Experiments

### Describe in Detail

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 ta

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## Question number: 85

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

### Describe in Detail

Explain the Case of rejection of for Analysis of variance for one way classification.

### Explanation

**Case of rejection of** **:**

is rejected. This means that at least one is different from other effects which is responsible for the rejection. So objective is to investigate and find out such and divide the population into groups such that the means of populations within the

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## Question number: 86

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

### Describe in Detail

Explain One-way classification with fixed effect linear models of full rank

### Explanation

- The objective in the one way classification is to test the hypothesis about the equality of means on the basis of several samples which have been drawn from unilabiate normal populations with different means but the same variances.
- Let there be p unilabiate normal populations and samples of different sizes are drawn from each of the population
- Let

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## Question number: 87

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

### Describe in Detail

Describe Latin square.

### Explanation

**Latin square:**

- A Latin square of order p is an arrangement of p symbols in cells arranged in p rows and p columns such that each symbol occurs once and only once in each row and in each column.
- For example, to write a Latin square of order 4, choose four symbols – A, B, C and D. These letters are Latin letters which are used as symbols. Write the

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## Question number: 88

» Design and Analysis of Experiments » Analysis of Covariance

### Describe in Detail

To compare the heights of Soprano, Alto, Tenor and Bass singers, data have been collected from the NY Choral Society in (singers). Determine whether these four groups have the same mean height. Use α=0.05.

### Explanation

- We use ANOVA to answer this question as we have a response variable (heights) measured across a categorical variable (Singers) of more than two levels (Soprano, Alto, Tenor, and Bass)
**H**_{o}**:**is that the mean heights of the four types of singers are equal. In statistical notation this is:

**H**_{a}**:**is that at least one of these means diff

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## Question number: 89

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

### Describe in Detail

Describe completely randomized design.

### Explanation

**Completely randomized design (CRD):**

The CRD is the simplest design. Suppose there are v treatments to be compared

All experimental units are considered the same and no division or grouping among them exist.

In CRD, the v treatments are allocated randomly to the whole set of experimental units, without making any effort to group the experimental units

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## Question number: 90

» Design and Analysis of Experiments » Analysis of Covariance

### Describe in Detail

A clinical psychologist has run a between-subjects experiment comparing two treatments for depression (cognitive-behavioral therapy (CBT) and client-centered therapy (CCT) against a control condition. Subjects were randomly assigned to the experimental condition. After 12 weeks, the subject’s depression scores were measured using the CESD depression scale. The data are summarized as follows:

Use a one-way ANOVA with for the test

### Explanation

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

Intermediate steps in calculatin

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