Agriculture Reference
In-Depth Information
essentially an exercise with variance. We know
that variance does not depend on the change of
origin but depends on the change of scale. So if
we add or subtract a constant quantity to each and
every observation of the data set to be subjected
under analysis of variance, there should not be
any effect of such mathematical manipulation
(change of origin). But definitely there will be
effect of change of scale on analysis of variance.
The following examples demonstrate the above
two factors.
1. Analysis of variance with change of origin
2. Analysis of variance with change of scale
3. Analysis of variance with change of both
origin and scale
Let us take the following example to demon-
strate the above.
Variety
Average germination %
V5
92.333
V4
86.333
V3
72.333
V8
66.333
V1
55.000
V2
27.667
V7
18.000
V6
16.667
It is found from the above two analyses that
there is no difference in results and conclusion.
Thus, from the above three analyses based on
transformation principle, it can be inferred that
results and conclusion may or may not remain
the same. But it is always wise to take care of
necessary transformation, wherever required.
Effect of Change in Origin and Scale in
Analysis of Variance
:
Sometimes in real-life situation, we come
across with data which are very large or very
small in nature, thereby posing difficulty in tak-
ing up statistical analysis further. Analysis of
variance, as has been mentioned earlier, is noth-
ing but the partitioning of variance due to assign-
able causes and non-assignable causes. Thus, it is
Example 10.7.
The following table gives the
yield (kg/plot) of four different varieties of
onion in three different irrigation treatments.
Analyze the data (a) with change of origin to
100 kg/plot and (b) with change of origin to
100 kg/plot and scale to 8 kg/plot, and comment
on the effect of change of origin and scale on the
results of ANOVA.
(A) Analysis with original data
Variety 1
Variety 2
Variety 3
Variety 4
I 1
181
195
185
110
184
197
184
125
182
198
187
115
I 2
224
245
228
145
225
240
227
135
223
247
229
142
I 3
200
210
205
130
201
208
202
132
202
207
204
131
Summary
Variety 1
Variety 2
Variety 3
Variety 4
Total
I1
182.333
196.667
185.333
116.667
170.250
I2
224.000
244.000
228.000
140.667
209.167
I3
201.000
208.333
203.667
131.000
186.000
Average
202.444
216.333
205.667
129.444
(continued)
