Research Methodology - Dr. Krishan K. Pandey
Research Methodology - Dr. Krishan K. Pandey Research Methodology - Dr. Krishan K. Pandey
Analysis of Variance and Co-variance 271 The graph indicates that there is a significant interaction because the different connecting lines for groups of people do cross over each other. We find that A and B are affected very similarly, but C is affected differently. The highest reduction in blood pressure in case of C is with drug Y and the lowest reduction is with drug Z, whereas the highest reduction in blood pressure in case of A and B is with drug X and the lowest reduction is with drug Y. Thus, there is definite inter-relation between the drugs and the groups of people and one cannot make any strong statements about drugs unless he also qualifies his conclusions by stating which group of people he is dealing with. In such a situation, performing F-tests is meaningless. But if the lines do not cross over each other (and remain more or less identical), then there is no interaction or the interaction is not considered a significantly large value, in which case the researcher should proceed to test the main effects, drugs and people in the given case, as stated earlier. ANOVA IN LATIN-SQUARE DESIGN Latin-square design is an experimental design used frequently in agricultural research. In such a design the treatments are so allocated among the plots that no treatment occurs, more than once in any one row or any one column. The ANOVA technique in case of Latin-square design remains more or less the same as we have already stated in case of a two-way design, excepting the fact that the variance is splitted into four parts as under: (i) variance between columns; (ii) variance between rows; (iii) variance between varieties; (iv) residual variance. All these above stated variances are worked out as under: Variance between columns or MS between columns Variance between rows or MS between rows Variance between varieties or MS between varieties Residual or error variance or MS residual Table 11.8 2 2 di bg b g 2 2 bg Tibg T ni n br − 1g 2 2 bg Tvbg T nvn bv − 1g TjT ∑ − nj n = c − 1 = ∑ − ∑ − = = = = SS SS SS between columns d.f. between rows d.f. between varieties d.f. Total SS – ( SS between columns + SS between rows + SS between varieties) = * ( c – 1) ( c – 2) * In place of c we can as well write r or v since in Latin-square design c = r = v. Contd. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○
272 Research Methodology 2 2 where total T SS =∑dxiji bg − n c = number of columns r = number of rows v = number of varieties Illustration 4 Analyse and interpret the following statistics concerning output of wheat per field obtained as a result of experiment conducted to test four varieties of wheat viz., A, B, C and D under a Latinsquare design. Solution: Using the coding method, we subtract 20 from the figures given in each of the small squares and obtain the coded figures as under: Rows Column totals 1 2 3 4 C C A B D A B D Fig. 11.2 (a) Squaring these coded figures in various columns and rows we have: 25 19 19 17 B D A C 23 19 14 20 A C D B 20 21 17 21 D B C A 20 18 20 15 Columns Row totals 1 2 3 4 5 –1 –1 –3 0 B D A C 3 –1 –6 0 –4 A C D B 0 1 –3 1 –1 D B C A 0 –2 0 –5 –7 8 –2 –10 –7 T = –12
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272 <strong>Research</strong> <strong>Methodology</strong><br />
2<br />
2<br />
where total<br />
T<br />
SS =∑dxiji bg −<br />
n<br />
c = number of columns<br />
r = number of rows<br />
v = number of varieties<br />
Illustration 4<br />
Analyse and interpret the following statistics concerning output of wheat per field obtained as a<br />
result of experiment conducted to test four varieties of wheat viz., A, B, C and D under a Latinsquare<br />
design.<br />
Solution: Using the coding method, we subtract 20 from the figures given in each of the small<br />
squares and obtain the coded figures as under:<br />
Rows<br />
Column<br />
totals<br />
1<br />
2<br />
3<br />
4<br />
C<br />
C<br />
A<br />
B<br />
D<br />
A<br />
B<br />
D<br />
Fig. 11.2 (a)<br />
Squaring these coded figures in various columns and rows we have:<br />
25<br />
19<br />
19<br />
17<br />
B<br />
D<br />
A<br />
C<br />
23<br />
19<br />
14<br />
20<br />
A<br />
C<br />
D<br />
B<br />
20<br />
21<br />
17<br />
21<br />
D<br />
B<br />
C<br />
A<br />
20<br />
18<br />
20<br />
15<br />
Columns Row totals<br />
1 2 3 4<br />
5<br />
–1<br />
–1<br />
–3<br />
0<br />
B<br />
D<br />
A<br />
C<br />
3<br />
–1<br />
–6<br />
0<br />
–4<br />
A<br />
C<br />
D<br />
B<br />
0<br />
1<br />
–3<br />
1<br />
–1<br />
D<br />
B<br />
C<br />
A<br />
0<br />
–2<br />
0<br />
–5<br />
–7<br />
8<br />
–2<br />
–10<br />
–7<br />
T = –12
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