Sampling methods
1. Statistical Farm Structure Survey 2013 is performed applying:
1.1. Statistical survey on all agricultural companies and enterprises;
1.2. Sampling methods for the farmers‘and family farms.
2. The population of farmers‘ and family farms – farms with the utilised agricultural area
of one or more hectares or those with the utilised agricultural area of less than one hectare and
annual agricultural income of no less than LTL 5000 (hereinafter referred to as “farms larger than 1
ha”).
3. A simple random sample is applied for the farms larger than 1 ha. The sample size is
45000.
4. For the selection of the farmers‘and family farms larger than 1 ha stratified sample
method is applied.
5. Standard output and municipalities are used for stratification. The standard output for
every holding is calculated from the data of the previous years (from the statistical register) before
the stratification.
5. Sampling method:
5.1. Let us denote the population of the farmers’ and family farms by the variable U.
Population is divided into H intervals of the equal length. First of all, the population strata H is
created and denoted UH, which consists of:
5.1.1. the farms with standard output greater or equal to 27622.4 LT (about 8000 euro);
5.1.2. organic farms;
5.1.3. the farms with special crops (nut trees, nurseries, perennial plants for twining,
weaving, energy purposes, flax , oil crops, grain maize, tobacco, hops, aromatic, medicinal and
culinary plants, plants for seeds and seedlings, fibre plants) or ostriches.
5.1.4. Other holdings are grouped by standard output and after that by municipalities. If
number of farms in stratum is not enough for the statistical estimation, these farms are also added to
the stratum UH with the probability equal 1.
5.2. The farms are added to the population strata UH with the probability 1.
5.3. Other farmers’ and family farms U\UH are stratified by Standard output and
municipalities.
5.4. First of all, the margins into the strata of the Standard output have been selected. This
is done on the basis of the root of f rule. Let us consider this rule. Let us denote the population size
M, Standard output by x. Values of this variable x1,...,xM are divided into K equal intervals. fk –
relative frequency of the elements in the population belonging to the k-th interval, k=1,..., K. The
total:
𝑡𝑓 = ∑𝐾
(1).
𝑘=1 √𝑓𝑘 .
𝑡
𝑓
5.5. Divide tf into H-1 equal parts 𝐻−1
and find approximate points of division of tf :
k1,...,kH-1 such that:
𝒕
𝒌𝟐
𝒌𝑯−𝟏
𝒇
𝟏
∑𝒌𝒌=𝟏
√𝒇𝒌 ≈ ∑𝒌=𝒌
√𝒇𝒌 ≈ ⋯ ≈ ∑𝒌=𝒌
√𝒇𝒌 ≈ 𝑯−𝟏.
𝟏 +𝟏
𝑯−𝟐 +𝟏
(2).
5.6. The elements belonging to the first interval [1,k1], are appointed to the first stratum.
The elements belonging to the second interval [k1+1,k2], are appointed to the second stratum, and so
on, the elements belonging to the last interval [kH-2+1,kH-1], are appointed to the H-1 stratum.
Thus, population U is divided into strata U=U1⋃U2⋃...⋃UH. of size Nh, h=1,...,H, N=
N1+...+ NH, where h denoted the h – th stratum.
Let us denote the variance of x (𝑠ℎ2 ) and the mean of x (𝜇ℎ ) in the h – th stratum by
𝑠ℎ2 =𝑁
1
ℎ −1
1
∑𝑘∈𝑈ℎ (𝑥𝑘 − 𝜇ℎ )2 , 𝜇ℎ = ∑𝑘𝜖𝑈ℎ 𝑥𝑘 , ℎ = 1, … , 𝐻 − 1.
𝑁
ℎ
(3).
Suppose, that n is the sample size being selected, sh2 is the standard deviation of the
variable x in the h – th stratum, and k denotes the element which belongs to the h – th stratum 𝑘 ∈
𝑈ℎ . Then the Neyman optimal allocation is used to define the sample size in the stratum:
𝑁 𝑠
𝑛ℎ = 𝑛 ∙ ∑𝐻−1ℎ𝑁ℎ 𝑠 , h=1,...,H-1.
ℎ=1
ℎ ℎ
(4).
Accuracy of the estimator of total 𝑡𝑥 = ∑𝐻
ℎ=1 ∑𝑘𝜖𝑈ℎ 𝑥𝑘 is measured by its coefficient of
variation:
𝑐𝑣 (𝑡̂𝑥 ) =
1
2
𝑛ℎ 𝑠ℎ 2
𝐻−1 2
(∑ℎ=1 𝑁ℎ (1− ) )
𝑁ℎ 𝑛ℎ
𝑡𝑥
∙ 100%.
(5).
Using the f rule for a given H we calculate the boundaries of the strata that minimize the coefficient
of variation of the estimator of the total.
First of all, the population stratified into the H-1 strata by Standard output by the Neyman
optimal allocation (denoted by equation 4). After that the sample size in the production stratum nh
divided in to the l strata proportionally. Thus, sample size h in the stratum nh=nh1+nh2+...+nhL,
h=1,...,H.
Let us denote Nhl, h=1,...,H, l=1,...,L – the number of farms in the h stratum of the
production in l municipality, Nh=Nh1+...+NhL – the population size in the h stratum. Then
proportional allocation is denoted by formula:
𝑁ℎ𝑙
𝑛ℎ𝑙 = 𝑛ℎ ∙ ∑𝐿
𝑙=1 𝑁ℎ𝑙
, h=1,...,H, l=1,...,L.
(6).