Research Methodology - Dr. Krishan K. Pandey
Research Methodology - Dr. Krishan K. Pandey Research Methodology - Dr. Krishan K. Pandey
Analysis of Variance and Co-variance 279 198 = = 274. 40 0. 7216 Deviation of initial group means from Final means of groups in X (unadjusted) general mean (= 14) in case of Y Group I –7.40 9.80 Group II 0.40 22.80 Group III 7.00 35.00 Adjusted means of groups in X = (Final mean) – b (deviation of initial mean from general mean in case of Y) Hence, Adjusted mean for Group I = (9.80) – 0.7216 (–7.4) = 15.14 Adjusted mean for Group II = (22.80) – 0.7216 (0.40) = 22.51 Adjusted mean for Group III = (35.00) – 0.7216 (7.00) = 29.95 Questions 1. (a) Explain the meaning of analysis of variance. Describe briefly the technique of analysis of variance for one-way and two-way classifications. (b)State the basic assumptions of the analysis of variance. 2. What do you mean by the additive property of the technique of the analysis of variance? Explain how this technique is superior in comparison to sampling. 3. Write short notes on the following: (i) Latin-square design. (ii) Coding in context of analysis of variance. (iii) F-ratio and its interpretation. (iv) Significance of the analysis of variance. 4. Below are given the yields per acre of wheat for six plots entering a crop competition, there of the plots being sown with wheat of variety A and three with B. Variety Yields in fields per acre 1 2 3 A 30 32 22 B 20 18 16 Set up a table of analysis of variance and calculate F. State whether the difference between the yields of two varieties is significant taking 7.71 as the table value of F at 5% level for v 1 = 1 and v 2 = 4. (M.Com. II Semester EAFM Exam., Rajasthan University, 1976) 5. A certain manure was used on four plots of land A, B, C and D. Four beds were prepared in each plot and the manure used. The output of the crop in the beds of plots A, B, C and D is given below:
280 Research Methodology Output on Plots A B C D 8 9 3 3 12 4 8 7 1 7 2 8 3 1 5 2 Find out whether the difference in the means of the production of crops of the plots is significant or not. 6. Present your conclusions after doing analysis of variance to the following results of the Latin-square design experiment conducted in respect of five fertilizers which were used on plots of different fertility. A B C D E 16 10 11 09 09 E C A B D 10 09 14 12 11 B D E C A 15 08 08 10 18 D E B A C 12 06 13 13 12 C A D E B 13 11 10 07 14 7. Test the hypothesis at the 0.05 level of significance that μ1= μ2 = μ3 for the following data: Samples No. one No. two No. three (1) (2) (3) 6 2 6 7 4 8 6 5 9 – 3 5 – 4 – Total 19 18 28 8. Three varieties of wheat W 1 , W 2 and W 3 are treated with four different fertilizers viz., f 1 , f 2 , f 3 and f 4 . The yields of wheat per acre were as under:
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280 <strong>Research</strong> <strong>Methodology</strong><br />
Output on Plots<br />
A B C D<br />
8 9 3 3<br />
12 4 8 7<br />
1 7 2 8<br />
3 1 5 2<br />
Find out whether the difference in the means of the production of crops of the plots is significant or not.<br />
6. Present your conclusions after doing analysis of variance to the following results of the Latin-square<br />
design experiment conducted in respect of five fertilizers which were used on plots of different fertility.<br />
A B C D E<br />
16 10 11 09 09<br />
E C A B D<br />
10 09 14 12 11<br />
B D E C A<br />
15 08 08 10 18<br />
D E B A C<br />
12 06 13 13 12<br />
C A D E B<br />
13 11 10 07 14<br />
7. Test the hypothesis at the 0.05 level of significance that μ1= μ2 = μ3<br />
for the following data:<br />
Samples<br />
No. one No. two No. three<br />
(1) (2) (3)<br />
6 2 6<br />
7 4 8<br />
6 5 9<br />
– 3 5<br />
– 4 –<br />
Total 19 18 28<br />
8. Three varieties of wheat W 1 , W 2 and W 3 are treated with four different fertilizers viz., f 1 , f 2 , f 3 and f 4 . The<br />
yields of wheat per acre were as under:
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