Research Methodology - Methods and Techniques 2004

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 Research  Res earch Meth Methodol odology ogy Per acre production data Plot of land

Variety of wheat    A

B

C 

1

6

5

5

2

7

5

4

3

3

3

3

4

8

7

4

Solution: We

can solve the problem by the direct method or by short-cut method, but in each case we shall get the same result. We try below both the methods. Solution through direct method:  First we calculate the mean of each of these samples:  X 1 =  X 2 =  X 3 =

Mean of the sample means or

 X  =

=

6+7 +3 +8 4 5+5+3+7 4 5+4+3+4 4

=6 =5 =4

X 1 + X 2 + X 3 k 

6+5+4 3

=5

Now we work out SS  between  between and SS  within  within samples:

   

SS betwe between en = n1 X 1 − X

 2 + n2  X 2    

    − X     + n3  X 3 − X    2

2

= 4(6 – 5)2 + 4(5 – 5) 2 + 4(4 – 5) 2 =4+0+4 =8



SS wit within hin = ∑ X 1i − X 1



2

2

2

+ ∑ X 2i − X 2  + ∑ X 3i − X 3   ,

= {(6 – 6)2 + (7 – 6) 2 + (3 – 6) 2 + (8 – 6) 2} + {(5 – 5)2 + (5 – 5) 2 + (3 – 5)2 + (7 – 5)2} + {(5 – 4)2 + (4 – 4) 2 + (3 – 4)2 + (4 – 4)2} = {0 + 1 + 9 + 4} + {0 + 0 + 4 + 4} + {1 + 0 + 1 + 0} = 14 + 8 + 2 = 24

i = 1, 2, 3, 4