# ISS (Statistical Services) Statistics Paper IV: Questions 85 - 91 of 92

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## Question 85

### Describe in Detail

Essay▾

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 group are same. This can be done by pairwise testing of

Test

This can be teste…

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## Question 86

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### Describe in Detail

Essay▾

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 b…

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## Question 87

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### Describe in Detail

Essay▾

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 them in…

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## Question 88

### Describe in Detail

Essay▾

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)
• Ho: is that the mean heights of the four types of singers are equal. In statistical notation this is:

• Ha: is that at least one of these means differ, or can be written …

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## Question 89

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### Describe in Detail

Essay▾

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 90

### Describe in Detail

Essay▾

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 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: reject H0

ANOVA table:

 Source SS df MS F

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## Question 91

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### Describe in Detail

Essay▾

Suppose the yield from different plots in an agricultural experiment depend upon

1. (i) variety of crop

(ii) type of fertilizer

Both the factors are in the control of experimenter.

2. (iii) Soil fertility. This factor is not in the control of experimenter.

### Explanation

In order to compare the different crop varieties

• Assign it to different plots keeping other factors like irrigation, fertilizer, etc. fixed and the same for all the plots.
• The conclusions for this will be valid only for the crops grown under similar conditions with respect to the factors like fertilizer, irrigation etc.

In order to compare different f…

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