Orthogonality
Orthogonality exists when the condition Sf icicj=0
and Sf ici=0
for each equation.
| f i |
9/16 |
|
3/16 |
|
3/16 |
|
1/16 |
| c1 |
1 |
|
1 |
- |
3 |
- |
3 |
| c2 |
1 |
- |
3 |
|
1 |
- |
3 |
| c3 |
1 |
- |
3 |
- |
3 |
|
9 |
First to show that Sf ici
= 0:
| Sf ici when i |
= 1  9/16(1) + 3/16(1) + 3/16(-3) + 1/16(-3) = 0 |
| i |
= 2 9/16(1) + 3/16(-3) + 3/16(1) + 1/16(-3) = 0 |
| i |
= 3 9/16(1) + 3/16(-3) + 3/16(-3) + 1/16(9) = 0 |
Now to show that SSf icicj
= 0
i=1, j=2
(9/16)(1)(1) + 3/16(1)(-3) + 3/16(-3)(1)
+
1/16(-3)(-3) = 0
i=1, j=3
(9/16)(1)(1) + 3/16(1)(-3) + 3/16(-3)(-3)
+
1/16(-3)(9) = 0
i=2, j=3
(9/16)(1)(1) + 3/16(-3)(-3) + 3/16(1)(-3)
+
1/16(-3)(9) = 0
** The concept of orthogonal tests of hypothesis is
that each test 'stands alone' and the results of one
test does not influence another test.
| X2A = |
(a1 + a2 - 3a3 - 3a4)2 |
| 3n |
| X2B = |
(a1 - 3a2 + a3 - 3a4)2 |
| 3n |
| X2L = |
(a1 - 3a2 -3a3 + 9a4)2 |
| 9n |
