Page 52 - Contributed Paper Session (CPS) - Volume 5

CPS861 Madeline Dumaua C.
(1) Ratio of Absolute Bias to the Standard Deviation
One characteristics of a good estimator is unbiasedness, therefore it is of
interest to measure the degree of bias of the two estimators. The ratio of
absolute bias to the standard deviation of the estimator was considered to
determine if the computed bias is negligible or not, and it is defined as,

̂
|()|
(,σ) = × 100 (2.5.1)
̂
√()

If the absolute bias over the standard deviation of the estimator is less than
or equal to 0.10 then it can be said that the bias is negligible (Cochran, 1977).
(2) Relative Root Mean Square Error
In here, all possible samples were utilized to generate the statistical
properties of estimates. In particular, relative root mean
square errors were computed as:

̂
√()
= × (2.5.2)

where,
̂
̂
̂
() = () + {()} (2.5.3)

̂
̂
̂

() = () () − = = () (/) − (2.5.4)

=

̂
̂
̂
̂
̂
() = ∑ [() − ()] () = ∑ 1000 [() − ()] ( ) (2.5.5)
=1
=

̂
̂
() = () (/) (2.5.6)
=

̂
where () is the estimate of the total in a municipality m computed from

samples ( = 1, 2, … , 1000) and is the population total for municipality

.
According to Rao (2000), mean squared error (MSE) was used to measure
the accuracy and precision of an estimator. For comparison purposes Relative
Root Mean Square Error (RRMSE) was considered to measure accuracy and
precision of the estimates. An estimator which has the minimum relative root
mean square error was considered as the more precise estimator to estimate
the total number of farm equipment and facilities.
(3) Coefficient of Variation In terms of reliability of the estimate, coefficient
of variation was used and these were computed as,

̂
̂
= (√()/() ∗ 100 (2.5.7)

It was used to indicate the “goodness” of the estimates for the total number
of farm equipment and facilities. An estimator with smallest value of coefficient
of variation was considered as the more reliable estimator to estimate the total
number of farm equipment and facilities.
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