ISS (Statistical Services) Statistics Paper IV: Questions 80  88 of 92
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Question number: 80
» Design and Analysis of Experiments » Randomized Block and Latin Square Design
Describe in Detail
Describe Randomized Block Design.
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 exper
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Question number: 81
» Design and Analysis of Experiments » Analysis of Covariance
Describe in Detail
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:
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Question number: 82
» Design and Analysis of Experiments » Analysis of Covariance
Describe in Detail
Using the following summary data, perform a one way analysis of variance using
Explanation
Calculating the remaining error (or within) terms for the ANOVA
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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 Twoway classification.
Explanation
Experiments with two or more factors: (Twoway 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 exac
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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
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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 populat
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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 Oneway 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
 L
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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 symbol
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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
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