Page 256 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 13: Test of Significance

Solution: Notes

Method 1 Method 2 Method 3
15 22 24
18 27 19
19 18 16
22 21 22
11 17 15
18
85 105 114

1. Sample mean is calculated as follows:
85 105 114
1 x = 5  17 2 x  5  21 3 x  6  19

2. Grand mean












15 18 19 22 11 22  27  18 21 17  24 19 16 22 15 18
= x 
16
304
=  19
16
3. Calculate variance between columns:
2 2
n x x x x  x x  n  x x 

5 17 19 -2 4 5 × 4 = 20
5 21 19 2 4 5 × 4 = 20
6 19 19 0 0 6 × 0 = 0
2
 i n  x   x = 40
1
2

 n x  x 
i
i
2 40
 =   20


k 1 3 1
Variance between column = 20
4. Calculation sample variance:
Training method -1 Training method -2 Training method -3
2
2
x x x x  x x x x  x x



2
2
15-17 (-2) = 4 22-21 (1) = 1 18-19 (1) = 1
2
2
18-17 (1) = 1 27-21 (6) = 36 24-19 (5) = 25
2
2
2
19-17 (2) = 4 18-21 (-3) = 9 19-19 (0) = 0
2
2
2
2
22-17 (5) = 25 21-21 (0) = 1 16-19 (-3) = 9
2
2
11-17 (-6) = 36 17-21 (-4) = 16 22-19 (3) = 9
2
2
15-19 (-4) = 16
2
2 2 2
 x x   70  x x   62  x x   60

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