Data Coding
While making out an analysis of the variance, it must be noted that the final quantity tested is a ratio and so dimensionless. That means the original measurement can be coded to simplify the calculations without the requirement for any subsequent adjustments of the results. The example below would illustrate the point.
Let us take 10 common questions in the illustration. The data coded are given below and the calculations are done as follow:
Coded data:
|
A(X1)
|
B(X2)
|
C(X3)
|
D(X4)
|
|
-2
|
+2
|
+8
|
+3
|
|
0
|
+1
|
+2
|
-1
|
|
+2
|
-1
|
+6
|
+2
|
|
-2
|
+4
|
-4
|
+6
|
|
-3
|
-6
|
-2
|
+5
|
|
ΣX1 = -5
|
ΣX2 = 0
|
ΣX3 = 10
|
ΣX4 = 15
|
|
X? - 1
|
0
|
2
|
3
|
Total sum of squares within the samples
= 15 + 58 + 104 + 30 = 208
Mean squares within the samples
= 208/(20 - 4) = 208/16 = 13
The benefit of coding can be appreciated better if we have big figures. Thus if the figures are:
|
Sample I
|
740
|
742
|
848
|
660
|
762
|
|
Sample II
|
745
|
650
|
758
|
664
|
754
|
|
Sample III
|
788
|
579
|
652
|
720
|
738
|
We can block this theorem each of the values and then carry out analysis of variance. This would very much simplify the calculations.