MCom I Semester Statistical Analysis Variance Study Material Notes ( Part 2 )

MCom I Semester Statistical Analysis Variance Study Material Notes ( Part 2 ) : Analysis of Variance in Randomised Blocks Analysis of Variance in Latin Squares Steps in Construction Latin Square  Miscellaneous Illustrations Examinations Questions Long Answer Questions Short Answer Questions Objective Type Questions  :

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Analysis of Variance in Randomised Blocks

Sometimes, we have to find out the analysis of variance with the help of data given in the form of Randomised Blocks. Therefore, in such a case, it would be essential to understand the randomized blocks.

The term ‘randomized block’ was derived from agricultural experimentation in which blocks of land were divided and randomization secured within each block, permitting a dual classification in which variance of two variables would be tested. One variable or classification would consist of several rows, each row representing an aspect of the classification and several columns consisting of an aspect of the second classification. Such a design permits estimating separately the variance of each of the two bases of classification, thus yielding two F-ratios, that is, two significance tests. Blocking is analogous to stratifying when several ‘variables’ or ‘treatments are applied to different blocks of the population. For example, if it is desired to test the difference between the yields when different kinds of wheat or fertilizer are applied. The difference in the yield may be attributed not only to the kinds of wheat sown or fertilizers applied, but also to differences in quality of the blocks of land. To isolate the effects of block, randomization is done i.e., assigning treatment at random to plots of each block of land. The blocks are so constituted that each contains as many plots as there are treatments to be tested, and one plot from each block is randomly selected for each treatment. Treatments are randomly assigned to units within units of each block. Suppose there are three treatments (A, B and C) to be assigned to four blocks of three plots, the arrangement may take the form :

Interpretation: The calculated value of F is 8.14 while the table value o is 3.88. The calculated value of F is greater than the table value of we reject the null hypothesis and conclude that there is a significant difference between the yields of the three varieties of wheat.

Analysis of Variance in Latin Squares

Latin-square design is an experimental design that is mostly used in agricultural experiments where nature plays a very important role and renders even fairly reliable results are very difficult to obtain. In agricultural investigations a number of experiments have to be carried out simultaneously and inferences have to be drawn under conditions which are different from those obtaining in other type of studies. For instance, an experiment has to be made through which the effects of four different varieties of fertilizers on the yield of a certain crop, say wheat, is to be judged. In such a case the varying fertility of the soil in different blocks in which the experiment has to be done must be taken into consideration otherwise the result obtained may not be very dependable because the output happens to be the effect not only of fertilizers but it may also be the effect of fertility of the soil. To overcome such difficulties, the Latin-square design is used.

Latin-square design is one wherein each fertilizer appears four times (if there are four varieties of fertilizers) but is used once and only once in each row as well in each column of the design. The following is a Latin-square design of experiment consisting of four types of fertilizers say A,

The above Arrangement has been made in such a manner that the effects of The above arrangement has been made in such a manner that have no bearing on the ultimate conclusions and difference in soil fertility would have no bearing on the ultimate arrangement of the fertilizers in the above inferences which are arrived at the arrangement of the fertili experiment is such that

EXAMINATION QUESTIONS

Long Answer Theoretical Questions

1 Explain the technique of analysis of variance for a two-way classification.

2. Explain briefly the technique of analysis of variance.

3. Write brief notes on the following:

(i) Randomized Block Design, and

(ii) Latin Square.

4. Explain the meaning and uses of analysis of variance. Describe the technique of analysis of variance for two-way classification.

5. what is an analysis of variance and what is the significance of its study ? Also explain the meaning of the F-coefficient used in this study,

6. Explain the meaning and uses of analysis of variance. How is an analysis of variance table set-up and how is a test based on it performed? What are the assumptions of that test ?

7. What do you understand by analysis of variance? Explain the basic assumptions in analysis of variance.

8. What is analysis of variance? Explain clearly the technique of analysis of variance for data with one-way classification.

Short Answer Theoretical Questions

1 Explain the technique of analysis of variance for a two-way classification.

2. Distinguish between one-way and two-way analysis of variance.

3. Explain the calculation procedure of variation between samples’ and variation within samples’

4. What do you understand by analysis of variance.

5. What is a total sum of squares in the analysis of variance ?

6. What are its components in one-way and two-way classifications? How are they calculated?

Objective Questions Which of the following Statement is True (T) or False (F):

1 The analysis of variance helps us to test the equality of two or more sample variances.

(False)

2. Analysis of variance can not be used when there are samples of unequal sizes.

(False)

3. If the calculated value of F > Foods then Ho is true.

(False)

4. There is only two sources of variance one-way classification between the samples and within the samples.

(True)

5. In a one-way classification value of MSB is always divided by the value of MSW.

(False) Fill in the blanks :

1 If the calculated value of F F 0,05 then H, is ……..

2. The analysis of variance helps us to test the equality of two or more sample

3. There are ……. source of variance for SST in two-way analysis of variance.

4. In one-way classification, the value of MSW is only divided by the value of MSB. when the value of ………. > value of.

5. In one-way classification value of ……… is always divided by the value of.

Ans. (1) True, (2) Means, (3) Three, (4) MSW, MSB, (5) Greater variance, Smaller variance.

Variance Study Material