Page 375 - Invited Paper Session (IPS) - Volume 2

IPS280 VEUN, Thy et al.
1, … , − 1, where was determined with Neyman Allocation as: =
ℎ
ℎ
ℎ ℎ (Eq. 1), are satisfied.
∑ −1 ℎ ℎ
ℎ=1
̅
2′
Step 2: Calculate ′ , ′ and for these boundaries, for ℎ = 1, … , − 1.
ℎ
ℎ,
ℎ
′′
′′
Step 3: Replace the initial sets of boundaries by , … , −1 ,
1
′2
′
′
− + √ −4 ′
ℎ
ℎ
ℎ ℎ
′′
where = 2 ′ , ℎ = 1, … , − 1(Eq. 2) (see more details in
ℎ
ℎ
Lavallée and Hidiroglou (1988, p.38)).
Step 4: Repeat steps 2 and 3 until two consecutive sets are either identical
or differ by negligible quantities.
Kozak algorithm was also used in conjunction with this method in the
evaluation of each stratum’s sample size as in Eq. (1), and to control for the
constraints as stated in step 1. Kozak algorithm was used in this case
because it often provides smaller sample size requirement than others, such
as Sethi algorithm, in the case of this studied population.
2) The Cumulated Root Frequency Method of Dalenius and Hodges
(CDH): This non-iterative was also used to calculate the optimum stratum
breaks in the values of the stratification variable. Because there is no precise
rule concerning the optimal number of classes, the Sturges’ formula was
used as the approximation to the number of classes K. Similar to LHK, the
determination of the minimum sample sizes within each stratum were
calculated basing on the same specified levels of precision and allocation
rule together with the determination of stratum bounds.
3) The Geometric Stratification Method of Gunning and Horgan
(GGH): This method is one of the noniterative methods that is extremely
convenient in the implementation of finding the stratum breaks using only
the minimum and maximum values of stratification variable to obtain the
boundaries. According Gunning and Horgan (2004), the stratum bounds
are the terms of geometric progression: = , for ℎ = 0,1,2, … , , where
ℎ
ℎ
= a (the minimum value of number of households within the village of
0
respective province), and = (the maximum value of number of

households within the village of respective province).
The stratification package in R was used as an aid in finding the
optimum stratum boundaries and the minimum sample sizes in each
stratum as well as the overall sample size of each province under the same
specified levels of precision, and under the same allocation rule. The take-
none and take-all strata were not set for LHK.
Because the sampling design was done through a multistage sampling
design rather than a direct element sampling, the effect between this
complex sampling and a simple random sampling schemes shall be taken
into account in the sample size determination. The design effect (deff) was
used to account for this effect. For this accounting, the preliminary sample

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