Page 51 - Contributed Paper Session (CPS) - Volume 5

CPS861 Madeline Dumaua C.

synthetic estimate. This means, that there are a total 32 possible samples
that can be generated in estimating the total number of farm equipment and
facilities per household farmer at the provincial level. Each provincial sample
will be in the form: = { }, = 1,2, … , ; = 1,2, … ,32. For instance, if =

5 , a possible sample would be = { , , , , , , }. Each of the
48
52
34
11

21
possible provincial samples was generated be selecting one sample from each
municipality independently and with equal probability.
The synthetic estimates at the municipal level are given by

∗ = ( ) ∗

where is the total number of households at the municipal level, is the

total number of households at the provincial level and is the estimate of

total number of farm equipment and facilities at the provincial level. This
estimator works under assumption that the municipality have the same
characteristics as the province and is therefore biased. However, the degree of
bias decreases as the ratio of the variables in the province becomes identical
to the ratios in the municipality (Du-Quiton et.al., 1999).

2.4 Direct Design Based Estimator
The direct estimates for the total farm facilities and equipment per
municipality for all the four pilot provinces were computed. The direct
estimator for the total farm facilities and equipment for the 2002 CAF is
defined as:
ℎ
̂
̂
= ∑ (2.4.1)
ℎ

=1

̂
where, = ∑ ℎ (2.4.2)
ℎ

=1

= municipality index = systematic sample
= barangay index = stratum index
= / = total number of strata (ℎ = 1, 2, 3)
ℎ
ℎ
ℎ
stratum 1: contains barangays included in the sample with certainty
stratum 2: includes barangays sampled in the 1991 CAF
stratum 3: includes barangays not sampled in the 1991 CAF

2.5 Evaluation of Estimates
Estimates produced using synthetic and direct design-based estimators
were evaluated in terms of their accuracy, precision and reliability. The
criterions considered in the study in the study include the ratio of the absolute
bias to the standard deviation, Relative Root Mean Square Error (RRMSE), and
Coefficient of Variation (CV). Thus, estimates were evaluated and compared
using the following properties:

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