1WO AREA FRAMES
FOR SAMPLING OF AGRICULTURAL IA1'ID
IN NEPAL
by
NIRMAL MAN PRADHAN
Institute of Statistics
Mimeograph Series No. 1117
Raleigh - May 1977
iv
TABLE OF CONTENTS
Page
'I
NEPAL - AN INTRODUCTION
1.1
1.2
1.3
1.4
1.5
1.6
2
1
..
. . . . . . . ·· ·· ·· ·· ·· ·· ·· ·· · · ·
····
··
···.
····· .
····
3
4
5
•
• • • •
• • • • • •
• • • • •
• • • •
Measurement •
5
5
7
8
,8
9
10
16
SAMPLE DESIGN AND CALCULATIONS
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
4
1
1
2
CONSTRUCTION OF AREA FRAME IN KATHMANDU VALLEY
2.1 The Kathmandu Valley • • • • • •
2.2 Coverage by Area Frame •
•
2.3 Cadastral Survey • • •
2.4 Cadastral Information
2.5 Land Classification and Units of
2.6 Cadastral Map
2.7 Area Segment • • • • • •
3
1
Introduction
Land Use
Administrative Division
Topography and Climate
Population and Its Distribution
Agriculture and Its Cropping Pattern
Analysis of Variance of Sample Data
Sample Size for a Specified Precision
• • • • • •
Separate Ratio Estimate and Its Sampling Variance
Combined Ratio Estimate and Its Sampling Variance
Cos t Func t10n
. . . . . . . . . . . . . . . . . . .
Determination of Sample Size Given Cost Constraint
Optimum Sample Allocation Over Strata
• • • •
Optimum Size of Area Segment for Rice Crop Survey
Economics of Statistical Precision • • • • • • • •
Price Elasticity of Demand for Rice in Nepal • • •
Welfare Loss and Net Benefit-Cost Ratio
Due to Improvement in Precision
.
•
• • •
• • •
SAMPLING SEGMENTS ON AERIAL PHOTOGRAPHS •
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
16
16
21
24
25
26
28
29
31
35
35
39
Collecting Agricultural Statistics •
• • • •
Comparison of Two Types of Area Frame Materials • • . •
Updating of Aerial Photographs •
. . . • • • •
Construction of Area Frame •
Stratification
• • • •
Paper Strata . •
• • • •
Area Segment • •
Sample Selection Procedure of Area Segments
39
39
40
41
42
45
46
47
Sam'ple Size
49
. . . . . . . . . . . . . . . . . . . .
Collection of Crop Area Statistics in the
Selected Area Segment
4.11 Estimation Procedures • • • . • • • • • .
50
51
v
TABLE OF CONTENTS (continued)
Page
5
SUBSAMPLING AREA SEGMENTS •
53
5.1 Construction of Area Frame for Two Stage Sampling
5.2 Method of Estimating Area Under Rice • • • • • • • •
5.3 Problem Involved in Estimation When Cultivated Area
in Each Stratum is Not Known • •
5.4 Estimation Sample Variance • • •
5.5 Hypothetical Problem • • • . • •
5.6 Estimation of Total Rice Acreage
5.7 Sample Variance of the Estimator .
6
SUMMARY AND CONCLUSIONS •
....
53
54
56
57
58
59
66
68
7 LIST OF REFERENCES
70
8
71
APPENDICES
8.1
8.2
8.3
8.4
8.5
8.6
8.7
Selected Area Segments (40 ha. size) •
Sample Data for Variance Comparisons • .
Summary Statistics for Variance Comparisons • • • • • •
Analysis of Variance of Rice Land (Y) as a Proportion
of the Cultivated Land (X) for a 60 Hectare Area
Segment (optimum size)
• • • • • • • • • •
Survey Costs • • • • • •
• • • • • • • • • •
Variable Cost Assessment for 40, 60 and 80
Hectare Area Segment •
• • • •
Formation of 40 Hectare Area Segment. • . • . • • • ••
72
73
77
78
79
81
82
vi
LIST OF TABLES
Page
Population distribution in Kathmandu Valley (number of
persons in thousands and number of panchayats are
given in parentheses) • • • • • • • • • • • • • • •
5
Cultivated and noncultivated land in the districts of
Kathmandu Valley, areas in thousands of hectares • • • • ••
6
District level cultivated area available for the construction
of area frame, area in thousands of hectares • • • • • • ••
7
4.
Cadestral survey
7
5.
Basic distributional characteristics of rice land (Y),
total cultivated land (X), and their ratio (R=Y/X) on
19 area segments in Bhaktapur • • • • • • • • • • • •
17
Analysis of variance of rice land (Y) , as a proportion of
total cultivated land (X) on 19 area segments in
Bhaktapur
.
17
- se2 and N values for different area segments in the
y,
h
districts of Kathmandu Valley
18
Sample sizes required to attain 5 percent and 1 percent
coefficients of sampling variance for district
estimates of proportion rice land for three sizes
of area segments
• • • • •
• • • •
20
1.
2.
3.
6.
....
7.
8.
............. ......
.....
.........
2
2
Syh' sxh r n and Ph values for 60 ha. area segment
22
10.
Separate ratio estimates for rice acreage in Kathmandu Valley •
23
11.
Distribution of variances and standard errors of the
separate ratio estimates by size of area segment
22
12.
Estimation of R for the valley
24
13.
The ratio R, variances and standard errors of combined
ratio estimate by size of area segment
25
14.
Optimum allocation of sample size over districts of
Kathmandu Valley
• • • . • • • • . • • • • •
28
15.
Optimum sample allocation over districts of Kathmandu
Valley by area segment size • • • • • • • • • • • •
29
9.
Nh ,
~
vii
LIST OF TABLES (continued)
Page
16.
Optimum sample size, population proportion, in each
strata variance of ratios in Kathmandu Valley • •
30
Quantity of rice sold and it's per unit price in
Kathmandu Valley
• • • • • • •
• • • • • • • ••
34
Net welfare loss assessment at different levels of
statistical precision and price elasticity of demand
36
Measurement of survey cost to improve the precision
level from 5 percent to 1 percent in a 60 hectare
area segment of Kathmandu Valley
37
20.
Benefit cost ratio
38
21.
Count unit identification, Kathmandu district •
45
22.
Sample data for the hypothetical problem
61
23.
Computation sheet for the estimation of area under rice • •
62
24.
Variation between ratios of subarea segments within strata
65
17.
18.
19.
•
viii
LIST OF FIGURES
Page
l.
Count unit and area segments •
48
2.
Selected area segment
53
3.
Magnified picture of area segment and subarea segments •
54
4.
Variance versus area segment size
32
• • • •
1
1. NEPAL - AN INTRODUCTION
1.1
Introduction
Having a total area of 54,717 square miles, Nepal is a hilly country
sandwiched between the Republic of India and the Peoples Republic of
China.
The location of the Himalayan Kingdom is best described by the
coordinates between longitudes 80° to 88° east and latitudes 26° to 30°
north.
The country is about 500 miles long, and the width fluctuates
between 90 to 150 miles.
1.2
Land Use
The total geographic area of the Kingdom is divided into the following
components:
forest accounts for 31.78 percent, land under perpetual snow
for 15 percent, waste land but reclaimable for 18.22 percent, cultivated
area (physical) for 14.06 percent and other land for 7.72 percent.
1.3
1
Administrative Division
Nepal is administratively divided into 14 zones and 75 districts.
A zone, being a bigger administrative unit, consists of five or six
districts.
A district is composed of village and town panchayats.
Using population households as a criterion of ward subdivision, each
village panchayat is divided into 9 ward units.
The process of sub-
division takes care of the even distribution of population over the
wards.
Depending upon the size of the local population, a town pancha-
yat may be subdivided into a large number of wards.
For all Cadastrally surveyed districts, Cadastral maps showing
panchayat and ward boundaries are available.
On the other hand, most
of the non Candastrally surveyed hilly districts do not have panchayat
lSource:
E.A.P.D. Ministry of Food and Agriculture, H.M.G. Nepal.
2
and ward maps.
The boundaries are arbitrarily determined by the local
panchayat people.
In recent years, the country has been broadly divided into strata
called "development regions."
The concept is based on the philosophy
that a district or even a zone is a small unit which cannot be developed
in isolation.
A set of districts, which are geographically close to
each other, have to share their natural and economic resources to become
a viable economic unit.
Hence, the country has been vertically (along
the width) subdivided into four development regions.
Each region in-
cludes three ecological regions called mountain, hills and terai.
This
is regional balance oriented subdivision.
1.4
Topography and Climate
In terms of topography and climate, the Himalayan Kingdom can be
broadly divided into three horizontal strips.
The top, central, and
bottom layers are called mountain, hills, and Terai regions, respectively.
1.4.1 Mountains
It includes higher hills between 8000 to 13,000 feet.
This region
has temperate climate; summer is cold, 'and the temperature in winter
falls below the freezing point.
Summer rainfall is dominant, and the
winter precipitation is generally in the form of snowfall.
hail, fog, and frost are very common.
on agriculture.
Thunderstorms,
Those factors put a constraint
Hundreds of thousands of hectares of pasture land are
available in this region, and it has a great potential for livestock
development.
Above 13,000 feet, the Tundra type of climate exists and
temperature always remains below 25°F.
3
1.4.2
Hills
North of Chure, the hilly belt is located between 3000 to 8000 feet
altitude.
This region has moist subtropical climate; it attains a maxi-
mum temperature of 90°F in summer, and the average temperature in winter
is about 50°F.
Summer rains are heavy, and the degree of rainfall de-
creases towards the western part of the hilly region.
1.4.3
Terai
Located on the south of Chure, the Terai belt (including inner Tarai)
runs east to west.
It is 25 to 35 miles wide.
The altitude varies from
600 to 3000 feet; humid tropical climate prevails in this region.
average temperature in summer exceeds 100°F.
oscillates between 54°F to 60°F.
The
The winter temperature
The summer rainfall varies from 70 to
35 inches as one moves from east to west.
The winter rainfall is not
evenly distributed, and western Terai gets brief westerly showers.
1.5
Population and Its Distribution
According to the 1971 population census, Nepal had 11.55 million
people.
The density of population was 211 people per square mile.
The
population, by 1976, is believed to have exceeded 12.5 million, and the
density of population has been pushed to 228 persons per square mile.
The demographic study on the population distribution and the rate of
growth indicated that Nepal's population in the 1960's (1961-1971) grew
at the rate of 2.07 percent per year.
the same period is as follows:
The population distribution for
4
Distribution of land and area
Region
Percent of land
to the total
Percent of populalation to the total
83
70
17
100
30
100
Hills and mountains
Terai
The plane land covers only 17 percent of the total area but accounts
for 30 percent of the population.
Seventy percent of the people stay in
the hills and mountains which constitutes about 83 percent of the total.
1.6
Agriculture and Cropping Pattern
Agriculture has been the dominant industry of Nepal.
About 14 per-
cent of the country's land resources has been used for cultivation.
More
than 93 percent of the people, in one way or another, are engaged in
agriculture.
Eighty percent of the total exports are of agricultural
origin, and it earns about that same percentage of the total foreign
exchange.
This sector contributed 69 percent to the gross domestic
product.
The cropping pattern of the country is
climate.
dicta~ed
by topography and
Food crops being the basic need of the people, have top priority
in terms of cultivation and it is reflected on the national land use
statistics.
area.
Food crops cover about 80 percent of the total cropped
In terms of area and production, rice is the leading crop, and
it is followed by corn, wheat, millet, and barley.
potatoes are also considered an important food crop.
Other than cereals,
Other than this,
oilseeds, Jute, sugarcane, and tobacco are the popularly grown cash
crops in Nepal.
5
2. CONSTRUCTION OF AREA FRAME FOR KATHMANDU VALLEY
·2~1
Kathmandu Valley
Situated at an altitude of 4500 feet above sea level,.the Kathmandu
Valley is composed of three districts:
(3) Bhaktapur.
(1) Kathmandu, (2) Lalitpur and
It covers an area of 218 square miles.
The Kathmandu Valley forms only 0.40 percent of the total land area
but accounts for 4.68 percent of the country's population.
Among the
cities of Nepal, Kathmandu has the largest urban concentration, followed
by Lalitpur and Bhaktapur.
Table 1.
Population distribution in Kathmandu Valley (number of persons
in thousands and number of panchayats are given in parentheses)
District
Towns
Kathmandu
150 (1)
204 (82)
354 (83)
Lalitpur
59 (1)
96 (39)
155 (40)
Bhaktapur
40 (1)
70 (21)
110 (22)
Totals
249 (3)
370(142)
619(145)
Source:
Villages
Total
Central Bureau of Statistics, Population Census, 1971.
2.2
Coverage by the Area Frame
The land survey department conducted a Cadastral survey of Kathmandu
Valley in the early 1960's.
To construct the area frame, the statistics
division staff of the Food and Agricultural Marketing Services Department
calculated the area totals at the subsection, wards panchayat and district
level.
The following table presents the cultivated and non-cultivated
land in each district of Kathmandu Valley.
6
Table 2.
Strata
No.
Cultivated and non-cultivated land in the districts of Kathmandu Valley (areas in thousands of hectares)
District
Cultivated
land
1
Kathmandu
24.00
9.51
33.51
2
Lalitpur
13.96
12.96
26.92
3
Bhaktapur
8.49
3.68
12.17
46.45
26.15
72.60
Total
Source:
Non-cultivated
land
Total·
Agricultural Statistics Division, Food and Agricultural Marketing
Services Department, HMG Nepal.
The population concentration of Kathmandu Valley is located in city
or town panchayats.
These are defined on the Cadastral maps.
The area
within the city limits will sooner or later be covered by urban dwelling.
So, the three city panchayats are deleted from the area frame.
Due to
one reason or the other a few wards are found to be uncovered or missing
since their field books are not available.
2
So the area frame included
all panchayat and wards for which field books were readily available.
The following table presents the cultivated area that has been used for
the construction of the area frame.
2
This term is used to indicate original record book, in which land
survey team has recorded all information on the parcel of land.
7
Table 3.
District level cultivated area available for the construction
of area frame (areas in thousands of hectares)
S. No.
District
Cultivated
area
Others
Total
1
Kathmandu
21.92
11.59
33.51
2
Lalitpur
11.83
15.09
26.92
3
Bhaktapur
8.17
4.00
12.17
Total
41.92
30.68
72.60
Source:
Agricultural Statistics Division, Food and Agricultural Marketing
Services Department, HMG Nepal.
2.3
Cadastral Survey
Land tax is one of the major sources of public revenue in Nepal.
To
update land records and modernize the land tax system, His Majesty's Government of Nepal (HMG) started Cadastral Survey in the early sixties.
The
project deals with land classification, measurement of area, recording of
Cadastral information, and preparation of Cadastral maps.
The land survey department has already completed Cadastral Surveys
in 34 districts.
The survey work in 4 districts is in process.
The
following table gives information on the status of the Cadastral survey
work.
Table 4.
Cadastral Survey
Rel:!:ion
Hills & mountains
Terai & inner terai
Total
Source:
No. of Cadastrally surveyed
districts
12
No. of non~Cadas- No. of distrally surveyed
tricts under
survey
districts
37
4
53
22
22
34
Total
37
4
75
Agricultural Statistics Division, Department of Food and Marketing
Services Department, HMG Nepal, 1976.
8
2.4
Cadastral Information
A district consists of panchayats.
based on three factors:
The panchayat boundaries are
(1) size of the population, (2) topography, and
(3) permanent, natural and identifiable locations, such as rivers, roads,
mountain ridges, etc.
chayat into wards.
The same criteria are used to subdivide the pan-
Depending upon its size and topography, a ward may
be subdivided into subarea segments (of a ward).
Each and every piece
of land is measured on the ground, and the following information is
recorded.
(1) Name of the district, panchayat and ward
(2) Survey number
(3) Parcel number
(4) Area of the parcel by classification of land
(5) Land use of the parcel (cropland, fruit)
(6) Name of the cultivator
(7) Government owned land
(8) Uncultivated land (temple, ponds, roads, rivers, forest, etc.)
From the above information, Qne can ,easily compute the area of a cultivated subsection level (subward).
2.5
Land Classification and Units of Measurement
There are only two classes of land, so the cultivated land should
either belong to low land or upland.
The low land has' four subcategories
abbal, doyam, sim and chahar, whereas the upland has only two subclasses,
3 4
abbal and doyam. '
3LoW land refers to partially or fully irrigated, leveled, rice
growing land.
~pl~nd
rainfall.
refers to slopeland of which the cultivation depends upon
9
In non-Cadastrally surveyed hilly districts, there is no standard
unit of area measurement.
Some areas have the area measurement in terms
5 6 In Kathmandu Valley, land is
of seed units, others have ha1ee.'
measured in terms of ropani, a ropani being an area of 74' x 74' or about
one-twentieth of a hectare.
2.6
Cadastral Maps
A ward is the smallest unit, but the survey team, due to topographic
reasons or heterogeneous characteristics, further split it into subsections.
They prepare detailed maps for each subdivision, and a map
is known as a "subsection map."
These map materials are very important
for collecting area statistics of agricultural crops.
For all Cadastrally
surveyed districts, subsection maps can be purchased from land survey
department.
Some salient features of a Cadastral map are as follows:
(1) Given the panchayat and ward, a Cadastral map can determine
the exact location and boundary of an area segment.
(2) Cadastral maps simplify the job of collecting area statistics
and saves a lot of time and money.
(3) A subsection map consists of small plots of land units called
parcels. The shape and size of each parcel is drawn on the map.
5The areas that use seed units is the area covered by a unit volume
(either mana or pathi) of seed. Depending upon the germination percentage,
sowing condition, etc. the coverage varies from one place to another.
6Ha1ee is the land area which is ploughed in a day by a pair of oxen.
The size of ha1ee depends upon: (1) number of hours worked, (2) skill and
activeness of the person who ploughs land, and (3) health condition of oxen.
10
2.7
Area Segment
2.7.1 Area Sampling
In sampling, the size of the population from which samples are
drawn should be known in advance.
In area sampling the total cultivated
area is divided into a definite number of identifiable sampling units
called area segments.
An area segment has fixed size and it is com-
posed of subsections which are cultivated subdivisions of a ward.
Probability sampling assumes prior knowledge of the probability of including every population unit in the sample.
For equal probability of
se1ection, the population units should be homogeneous in some characteristics.
To reflect this principle in area sampling, the size of the
sampling unit or area segments are made as uniform as possible.
In
actual practice, there exists some variation among the size of the area
segments but it does not adversely affect the basic principles of
sampling.
2.7.2
Coding
An area segment is made up of a set of ordered subsection area
totals.
Each and every subsection that goes with an area segment should
be identifiable in the area frame.
For this purpose, a five digit code
is used to identify a subsection. "The first two digits refer to the
serial number of the panchayat, the third one to ward number and the
last two digits correspond to the ordered serial number of the subsection,
within a ward.
The code 04705 refers to the fifth subsection area in
the seventh ward of the fourth panchayat in the list (panchayat arranged
in an alphabetical order).
These identities are helpful to locate the
11
Cadastral maps.
Subsections have been coded separately on individual
district basis.
2.7.3 Number of Sampling Units in the Population
by Size of Area Segment
A subsection as described earlier, is the subdivided component of a
ward.
It is actually composed of cultivated parcels which are measured
1 2 3
in terms of local units called ropani, ana and paisa. "
So the origi-
nal measure ofa subsection area is expressed in local units.
In order
to formulate area segments of definite size and standard measurement, each
subsection area has been converted into hectares.
Care has been taken to
keep the code (panchayat, ward, subsection) in proper order.
Finally
the information is transferred to the data card.
Given the district, the total cultivated area available for area
frame is known, if the size of the area segment is specified then one
can easily guess the total number of sampling units in the population.
The basic issue is focused on the discovery of that magic number.
Since
there is no immediate logic and justification to determine the area
segment size, a set of closely equispaced numbers (40, 60 and 80 hectares)
was chosen for investigation.
For each of these area segment sizes, it
is quite natural to expect different variances for estimating the total
rice area in the valley.
Given the survey cost constraint, we are
looking for the optimum size of the area segment which minimizes the
variance.
1
A ropani is equivalent to .0509 hectares.
2
An ana is the fraction of a ropani.
or one
a~a
Sixteen anas makes one ropani
is .0031 hectares of land.
3paisa is smaller than ana.
is about .0008 hectares.
Four paisa makes one ana, one paisa
12
To achieve this objective, a SAS computer program is used to perform
the following:
(1) Determine the number of sampling units (for 40, or 60, or 80
hectares) or area segments in the population for each district.
(2) Define each segment by code numbers.
(3) Corresponding to 40 ha. area segments, draw sample of size
30 each for Kathmandu and Lalitpur and 20 for Bhaktapur.
A part of the computer output is presented in the appendix.
2.7.4
Identification of a Selected Segment
As per the instruction, the computer has selected specified number
of samples by area segment size and also by district.
samples are identified by their code number.
The selected
Corresponding to each
selected sample, the computer specifies the codes (such as 03403 to
03501).
This implies that the selected segment begins with the third
subsection of the fourth ward of third panchayat and terminates with
first subsection of the fifth ward of the same panchayat.
All sub-
sections in between those two codes (for example all subsections in
ward four) are included in the selected segments.
2.7.5
Crop Area Survey Methods
The area frame provides the total cultivated area of the selected
segment, denoted by Y.
The rice acreage X, in the selected segment is
obtained from the area survey.
The two methods which are commonly used
for collecting area statistics are descxibed in the subsequent paragraphs.
(1) The list of cultivated parcels and the subsection level Cadastral
maps are the two basic materials required for conducting the area survey.
To locate parcels, subsection on the field, the Cadastral maps and local
13
panchayat people are the guides to the enumerator.
For each subsection,
-the enumerator should try to locate the starting point of the Cadastral
survey.
Once it is known, the boundary is subsequently identified on
the field.
The surveyor can just take a look at the field, a cluster of
parcels growing a single crop.
The boundary of the cluster is marked
on the map and he records the crop.
The procesR is continued' until the ob-
servations are completed, over the entire subsection.
The area survey
should cover all the subsections of the selected segment.
Rice is the dominating crop of late summer season in Kathmandu
Valley.
Except some groups of vegetable growing areas in isolation, most
of the low land area is under rice.
very common in the valley.
Growing rice in terrace land is also
Other contemporary crops are grown in dry
land slope land which is not suitable for rice crops.
In collecting
area statistics, the surveyor has to take full advantage of this monotype of cropping pattern.
However, due care should be taken that the artificial boundary
enclosing a bunch of parcels growing a single crop is properly identified
and recorded.
If the artificial crop boundary runs across a parcel then a
proportion is just estimated by eye observation.
The observations made on the map is translated into quantitative
measurement.
This is done on a predesigned form in which the list of
cultivated parcels, parcel number, area of the parcel is recorded.
The
parcel numbers, recorded on the map, help to materialize the qualitative
information into area measurement.
(2) In this alternative method, the crop area statistics is collected
on parcel to parcel basis.
As usual, the surveyor should first of all
14
locate the number orie parcel or starting point of the subsection on the
field.
The crop corresponding to each parcel is directly recorded on
the list of cultivated parcels (a predesigned form).
The information is
collected mainly on the basis of the knowledge of panchayat member or
knowledgeable local person.
Parcel number and name of the cultivator
are the guiding factors to collect area statistics.
In case of doubt,
the parcel has to be identified on the map and also on the field.
In short, it is stated that the method heavily re1ys on the knowledge
of the panchayat people.
People care what their neighbors are doing and
they follow the same pattern.
If a subsection has diversified multiple crops, then it is emphasized that this method, though time consuming and more expensive,
is worth adopting.
Otherwise, the former approach is much simplier and
quicker.
2.7.6
Sample Data on Rice Area
In order to determine the optimum size of the area segment for a
given cost, rice acreage data are needed for those selected area segment
samples.
Unfortunately, no survey of this type has been carried out
earlier so that the knowledge could be profitably used in the current
problem.
Hence the following assumptions have been made to construct
realistic appearing rice acreage data.
(1) Ninety to ninety-five percent of the total low land in the
selected segment grows rice crop.
The factor such as geographic location
of the panchayat, transportation and market facilities, and traditional
cropping patterns have been taken into account to delineate the area
15
allocation for vegetable and other crops.
The author's personal judge-
ment is however involved in this work.
(2) Rice cultivation in terrace land is very common in the Kathmandu
Valley.
Irrespective of low or upland rice crop is traditionally pre-
ferred.
So 20 to 30 percent of the upland has been accounted for rice
crop.
(3) Personal knowledge and some reports on previous agricultural
survey reports have been thoroughly used.
16
3.
3.1
SAMPLE DESIGN CALCULATIONS
Analysis of Variance of Sample Data
The joint distribution of rice land and cultivated area, segment by
segment, governs the sampling variability of the estimates.
to examine the nature of this joint distribution.
Thus we need
Sample data on culti-
vated area of the segment (denoted by X) and area under rice in the same
segment (denoted by Y) have been prepared for each of the districts in
the valley.
These data appear in the Appendix Table
of the form Y
data.
= ax,
A linear model
assuming no intercept, is fitted to analyze these
A part of the computer reprint corresponding to a 40 hectare
area segment for Bhaktapur district is reproduced in Table 5.
It should be noted that the mean square due to error in the ANOVA
Table 6 represents:
E(y
i
n-l
Rxi )2
in the formula for the variance of YR=
means and
X is
=
2
se
YX/x,
where y and x are sample
a P9pulation mean:
(I-f)
n
n
E
~l
A
(Y.~ - Rx.)
~
2
n-l
2
Information on s e ,y and population size N are required for computing
sample sizes and so they are presented in tabular form in Table 7.
3.2
Sample Size for Specified Precision
Given the information of Table 7 and a required coefficient of
variation (C.V.), the sample size required to meet the desired level of
e
e
e
Table 5.
Basic distributional characteristics of rice land (=Y), total cultivated land (=X), and their
ratio (R = Y/X) on 19 area segments in Bhaktapur
Variable
Mean
S.
deviation
Minimum
value
Maximum
value
S.E. of
the mean
Variance
C.V.
X
19
43.0402
15.2092
12.2853
68.8896
3.4892
231.3199
35.337
Y
19
29.5386
14.7540
3.6673
58.9384
3.3848
217.6809
49.948
R
19
0.6623
0.1808
.2985
0.9110
.0414
0.0327
27.309
Table 6.
Source
Model
Analysis of variance of rice land (=Y) as a proportion of total cultivated land (=X) on 19 area
segments in Bhaktapur
I
d.f.
1
I
Sum of squares
19459.2737
Error
18
1037.0326
Uncorrected
total
19
20496.3063
I
Mean square
19459.2737
I
F value
337.76
I
R2
.9494
I
C.V.
25.6963
57.6129
I-'
.....
Table 7.
- se2 and N values for d ifferent area segments in the districts of Kathmandu Valley
Y.
h
Area segment 40 ha.
Districts
Nh
I
se2
1-Y
Area segment 60 ha.
Nh
I
se2
1-Y
Area segment 80 ha.
2
Nh
se
Y
1
1-
1.
Kathmandu
556
71.9628
27.2943
371
134.1435
36.8832
278
159.8348
51. 7166
2.
Lalitpur
86.9680
17.8256
209
138.7355
27.6310
156
223.6257
36.247
3.
Bhaktapur
312
200
57.6129
29.5386
136
50.8406
41.4350
100
150.2257
58.2799
~
00
e
e
e
19
precision is calculated from the modified form of Cochran's formula (6.8)4
v(y )
(c.V)2
=
l-f
_~
=-n
y
where
s
y
3.2.2
2
= mean square due to error in the ANOVA table presented in the
e
appendix
= average
rice acreage per unit segment.
Sample Size for 40 Hectare Segment of Bhaktapur
Suppose the permissible margin of error in the estimate is 5 percent.
1
20'
That is, let C.V •
The formula is:
1-f
=-n
Ignoring the finite population correction (fpc) or setting 1-f = 1 and
solving for n yields:
s
n -
2
e •
-2
y
1
57·6129
-""(C-.V;;:;")""'Z =(29'5368)2 x 400
=
26 • 41 or n
=
26.
Hence a sample of 26 area segments is required to meet the 5 percent
margin of error in Bhaktapur district.
Let
C.V = 1 percent
i.e., C.V
1
= 100
•
The required sample size to meet one percent margin of error is given
by the following expression:
4"Samp1e Technique," W. G. Cochran, op cit. (6.8), p. 159.
20
n =
10000 x 57·6129
872·5289
660.
=
This sample size exceeds the population size so the adjusted sample size
is given by:5
n t·
n
= -,;;;;...=
1 +.!!
N
660
1 + 660
200
=
153·48,
or n' = 153.
It is customary that complete enumeration is preferred when the sample
size exceeds 75 percent of the total population.
is recommended in this case.
So complete enumeration
Working out the case for Bhaktapur and 40
hectares, thus describes and illustrates the procedure of computation
of sample size when the level of precision is specified.
It seems super-
f1uous to reproduce entire calculations for other area segments.
The
sample sizes to meet 5 percent and 1 percent levels of precision are
presented in the following table.
Table 8.
Sample sizes required to attain 5 percent and 1 percent coefficients of sampling variance for district estimates of
proportion rice land for three sizes of area segments
Area seg. = 40 ha.
1
5
(percent)
39
353
Districts
Kathmandu
La1itpur
ha.
109
280
Bhaktapur
26
153
--l1
82
Totals
174
786
124
426
5
Cochran,
OPt
cit., p. 75.
21
The following sections will illustrate two methods of ratio estimation, separate and combined. 6
The same data that have been used to esti-
mate the variances above will now be used as if they had been observed in
the course of a survey.
The problem is to make an estimate for the whole
valley and the question is whether to use a separate proportion for each
district or to use an overall proportion of rice land.
The calculation
show that the two methods are so nearly equal in variances that there is
little to choose between them and so one would use the combined ratio
method because of its overall greater stability.
3.3
Separate Ratio Estimate and Its Variance
Individual ratio estimates are formed for each district and they
are combined together to build an estimate for the whole valley.
is known as separate ratio estimates.
The total cultivated area for each
stratum or district needs to be known from the area frame.
ratio
Rh
This
The stratum
for each district is calculated from the sample data, given in
the appendix.
For a 60 hectare area segment the total rice area in the
valley is estimated by the formula:
Xh
=.6311 x 21920 +.4700 x 11830
+.7054 x 8170
= 25156.92
3.3.1
Separate Ratio Estimate
To compute the sample variance the essential data involved in the
calculations are presented in the following table.
6Cochran,
w.
G., op cit. 6·10 and 6·11, pp. 167 and 169.
22
Table 9.
2
2
N , n Syh sX'h R and value for 60 hectare area segment
h
h
h
District
Nh
[;J
30
2
syh
2
sxh
Syh
Sxh
Rh
I Ph
1-
Kathmandu
371
108.7850
110.9911
10.4300
10.5352
0.6311 .5315
2.
La1itpur
93.2851
13.5560
9.6584
0.4700 .5299
3.
Bhaktapur
30 183.7655
209
81.8055
136 -f.Q
106.1199
9.0446
10.3014
0.7054 .6357
Total
80
716
The sample variance of the estimate can be found as 7
3
v(YRS')
N2
= E h (1 f ) (2
A2
h=l n h - h Syh + Rb
=
4217'0333 x 79'3052 + 1247·0333 x 139'1556
+ 728'8000 x 51'0499
=
548232·4975
The standard error of the estimate is S.E.(y )
Rs
= 740.4272.
Similarly,
the estimates and the corresponding variances have been computed, and
the result is given in Table 10.
The sample variances and standard errors of the separate ratio
estimate corresponding to each of the area segments under consideration
are presented below.
Table 11.
Area ,40
hecta~e
Distribution of variances and standard errors of the separate
ratio estimates by size of area segment
V(YRS)
1082887'29
S .E. cYRS)
1040·62
60 hectare
548232.50.
740.43
80 hectare
997462.94
998.73
7
Cochran, W. G., op cit., 6'24, p. 168.
e
e
e
Table 10.
Separate ratio estimates for rice acreage, Kathmandu Valley
40 ha. segment
Rh
YRS =RhXh
60 ha. segment
Rh
YRS=RhXh
I
80 ha. segment
YRS=RhXh
I
Districts
Xh
l.
Kathmandu
21920
0.6396
14024·93
0.6311
13833.71
0.6327
13868.78
2.
Lali t pur
11830
0.4306
5096.48
0.4700
5560.10
0.4433
5244.24
3.
Bhaktapur
8170
0.6623
5411.85
0.7054
5763.11
0.6911
5646.29
Total
41920
24535.26
25.56.92
Rh
24759.31
N
W
24
3.4
3.4.1
Combined Ratio Estimate and Its Sample Variance
Combined Ratio Estimate
The combined ratio estimate due to Hansen, Burwitz and Gurney (1946)
is given by the following expression:
• X where X is the total cultivation are of the valley.
= R • X
=
3
E
h=l
-
~ Yh
3
=
E
h.=l
~ ~
To illustrate the application from the sample data of a 60 hectare area
segment, the following table is constructed.
Table 12.
Estimation of R for the 'llal1ey
-
I Yh=~Yh
-~
District
I~ I
1. Kathmandu
21920
371
36.8833
13683.70
59.7413
22164.02 }
2. Lalitpur
11830
209
27.6310
5774.88
58.2163
12167.21
3. B.haktapur
8170
136
41.4350
5635.78
59.1210
8040.46
~
Yh
Total
25093.74
~=Nn~
I R= ~~
.5922
42371. 69
The combined ratio estimate of the total rice acreage for the valley is
given by:
"
= Yst • X = 25093.74
41920
YRC
42371.69 x
x st
= 24825.02
25
3.4.2
Sam~le
Variance of Combined Ratio Estimate
A
A
Replacing Rh by R in the formula for variance in the separate ratio
estimate, one can get the expression for the variance of the combined ratio
estimate.
So, Table 9 is used to compute the variance for combined ratio
estimates.
(l-f ) (s2 +
h
yh
R?S2x
=
331306.5825 + 167486.0496 + 38548.8926
=
537341.5247
The standard error of the estimate is:
For 40, 60 and 80 hectare area segment size, the variances of the
combined ratio estimate is giYen in the following table.
Table 13.
The ratio i variances and standard errors of combined ratio
estimates by size of area segment
A
Area segment
R
v (YRC)
A
S.R. (YRC)
40 hectare
.5997
1090170.47
1044.12
60 hectare
.5922
537341.52
733.04
80 hectare
.5921
657947.69
811.14
3.5
Cost Function
In practice, a sample survey is commonly subjected to budgetary
constraints.
In this situation, the total sample size for the rice
surVey in the valley is determined by district-to-district survey cost
26
permits sample and overhead cost.
So the general principle is that given
the survey cost, the total sample size for the rice survey is determined
and the sample allocation over districts has to be done in such a way
that the variance of the estimate is minimized.
Consider a simple cost function of the form:
3
C=C
+ r Chn.
o
h=l
h
where C is the total cost, Co represents the fixed cost, and
sample size in the h th district of the valley.
unit sample in the h th district.
~
is the
C is the survey cost per
h
Wages and travel costs do not differ
from one district to another.
The survey cost is assumed to be uniform
for all strata of the valley.
That is C = C = C •
I
2
3
A slightly modified form of the above cost function is:
Here the survey cost per unit sample in the h th district is a combination
of fixed and variable cost.
In other words, the fixed cost is uniformly
distributed over the samples.
Actually, overhead cost dominates the variable cost when the sample
size is small.
For large sample survey the fixed cost for sample becomes
relatively small.
To illustrate the matter, fixed and variable cost
computation sheets are included in the appendix.
3.6 Determination of Sample Size, Given Cost Constraint
For the determination of optimum size of area segment for the rice
area survey, the three sizes corresponding to approximate area segments
of 40, 60 and 80 hectares will be compared.
In computing the three
27
sample sizes using cost constraints, only the variable survey cost is
taken into account.
The fixed cost is assumed to be uniform or constant
over the different segment sizes.
Suppose a lump sum of twenty-four thousand rupes is available for
conducting the rice acreage survey in Kathmandu Valley.
An amount of
Rs 5730 is allocated to fixed cost and Rs 18,270 goes to variable cost.
The variable cost assessment sheet, constructed by the author on the
experiences of previous sample surveys, estimates that the survey cost per
40 hectare size area segment is Rs 105. Therefore, the total sample cost
3
C = r C ~ and since C
1
h=l h n
= C2 = C3
• C
3
C
=C r
n.
h=l n
= Cn
18270 - 105n or n = 174.
If the same amount of money is used, then a smaller number of
samples for 60 and 80 hectare area segments will be available.
variable cost for surveying an area segment of 60 and 80
to Rs 133.95 and Rs 166.20, respectively.
The
hecta~es
comes
Given the survey cost, the
total sample size for 60 and 80 hectare segment becomes 136 and 109,
respectively.
8
Variable survey cost for 40 segment area is Rs 105, i.e., 7.00
mandays.
28
3.7
Optimum Sample Allocation Over Strata
The total sample sizes corresponding to the three area segment sizes
are those known.
A
of
~
The population strata sizes N and estimated variance
h
2
denoted by Sh(~) are used to allocate the sample sizes over strata
districts.
A
Given an area segment, the optimum sample size for the h th
stratum is given by the formula:
since survey cost C is taken as constant. 9 For a 40 hectare segment
h
size, the total sample size is 174.
The details of the computational
work is shown in the following table.
Table 14.
District
Optimum allocation of sample size over districts of Kathmandu
Valley.
I
Nh
I
n
Sh
Nh~
h
=
n • ~~,
E ~Sh
n
h
Kathmandu
556
.2087
116.0372
90.72
91
Lalitpur
312
.2255
70.3560
55.00
55
Bhaktapur
200
.1808
36.1600
28.27
28
222.5532
Total
174
Similar tables are required to compute sample size allocations for
60 and 80 hectare area segments.
for both segment sizes.
9
N and sh hectare values are different
h
The detailed computational work, being similar
Cochran, op cit. (5'19), p. 96.
~
•
29
to the above table, has not been presented, but the allocation of sample
size has been
Table 15.
Area segment
District
Kathmandu
La1itpur
Bhaktapur
Total
3.8
sho~
in the following table.
Optimum sample .a11ocation over districts of Kathmandu Valley
by area segment size
n=174
60 ha.
116.0372
70.3560
91
68.5237
n=136
n
h
73
55
42.1971
45
28.2516
35
36.1600
.-1.i
16.8232
-ll
13.2400
-!.§.
222.5532
174
127.5440
136
88.3624
109
40 ha.
NhS h
~~.
~
80 ha.
n=109
~~
46.8708
~
58
Optimum Size Area Segment for Rice Crop Area Survey
To compute the variance of the mean for 40, 60 and 80 hectare area
segment size under a given cost constraint, Table 17 is presented.
Let the estimated variance of the stratified sample mean for 40
hectares area segment be denoted by v(Y
st
' 40) then
ignoring fpc' the expression becomes
v(Y st ' 40)
= .2710 x .0436 + .0853 x .0509
91
+ .0351
55
x
28
S.E'(Y st ,40) = .0158
.0327 = .000250
Table 16.
Optimum sample size, population proportion in each stratum, variance of ratio in the
Kathmandu Valley
,
District
Area segment 40 ha.
N
Opt. W2• (-E.) 2 S2(R )
N
h N
h h
h
Area segment 60 ha.
2 Nh 2 2 "
Opt.
Wh=("N) Sh(Rh )
N
h
h
Area segment 80 ha.
N
Opt. W2= (-.1!.) 2
2 "
Sh(Rh )
N
h N
h
1. Kathmandu
92
.2710
.0436
73
.2685
.0341
58
.2710
.0284
2. La1itpur
56
.0853
.0509
45
.0852
.0408
35
.0853
.0328
3. Bhaktapur
29
.0351
.0327
18
.0361
.0153
16
.0351
.0175
w
o
e
e
e
31
Similarly, using the information given in the above table, the
estimated variances of the sample mean are:
v(Y st ' 60) = .000233
=
.0152
' 80)
=
.000251
, 80)
= .0158
S.E(yst ' 60)
~d
v(Y
S.E(y
st
st
From the above results, one concludes that:
v(y
st
, 60) < v(y
st
, 40) < v(y
st
,80)
So given survey cost, the optimum size of an area segment for rice
survey in Kathmandu Valley is 60 hectares.
3.9
Economics of Statistical Precision
The importance of accurate crop production statistics for agricultural planning and governmental decisionmaking process needs hardly
be stressed.
Erroenous information causes the government to formulate
inappropriate policies and make erroneous decisions.
These ultimately
result in some hazard to the economy for which the country has to pay
in one form or another.
In the sample survey the total error consists
of two types, namely sampling error and non-sampling error.
The error
arising from non-response, performance of the enumerator, arbitraty
definition of terms, faulty questionnaire, inaccurate measuring instrument, etc. could be stabilized at low ebb by carefully designing and
operating of the survey.
The sampling error can be reduced by taking
32
Figure 4.
Plot of variance against segment size for equal total cost of
survey
.015
o
Q
o
60
40
80
Area segment size
The superiority of the 60 ha. size should be viewed as a provisional
result.
Recall that the data on rice land were prepared using judgements
rather than actual measurements and this may have caused unrealistically
high correlation between X and Y.
33
considerably large samples.
In other words, the precision level of the
sample estimate can be adjusted by choice of adequate sample size.
Hence
marginal improvements in the accuracy of these statistics, according to
Hayami and Peterson, reduce social cost of mis-information which in turn
can be considered as an increase in net social welfare.
In order to estimate the amount of net welfare loss resulting from
either an erroneous over-estimation or under-estimation of production,
the authors have developed:
(a) an inventory adjustment model
(b) a production adjustment model under the following assumptions:
(1) the demand curve is linear and fully known
(2) quantity of rice supply is estimated in advance
(3) the government sets the price where quantity supplied
equals quantity demanded.
The net welfare loss in an inventory adjustment model is estimated
by the following expression:
= E2
1 .
pqex
where q is the true quantity of production, p is equilibrium price,
E
is
the error in the quantity of production reported as a proportion of the
true production, ex is the price elasticity of demand.
Since loss cannot
be negative, the absolute value of ex is used in computational work.
The Kathmandu Valley, as such, is believed to be self-sufficient
in tereal pro"duction.
Under normal weather conditions, 'it produces
For details, the paper entitled, "Social Returns in Public Information Services: Statistical Reporting of U. S. Farm Commodities," by
Yujiro Hayami and Willis Peterson, American Economic Review, March 1972
is referred.
34
about 56,000 metric tons of rice annually.
The valley, being a centre
of tourist attraction, receives a large number of foreign tourists and
also hosts short-term national visitors.
To feed these additional people,
the valley exports rice to the immediate neighboring districts.
A semi-
governmental agency (Nepal Food Corporation) operates the functions of
stabilizing low price, regulating supply, and holding buffer stocks of
rice.
This is a sort of artificial situation, and market forces have
little chance to operate freely.
Still, some of the factors such as
product differentiation, grain quality, and public tastes have kept
the market price somewhat higher than the controlled price.
To illustrate the situation, the quantities of rice sold by the
government agency in Kathmandu Valley for the past five years are presented in the following table.
Table 17.
Quantity of rice sold and its per unit price in Kathmandu
Valley
Item
Rice sale
1972/73
5995
(1661)
8848
(1661)
Year
1973/74
1974/75
1975/66
12419
(1661)
16573
(1661)
15697
(2250)
Fiqures in the parentheses represent price per unit metric ton of rice.
Source: Nepal Food Corporation, 1976 (unpublished collection).
It is now obvious that the current equilibrium price of rice for
Kathmandu Valley does not exist.
Also, there is a strong reason to
believe that the equilibrium price of rice in that region should exceed
controlled price of Rs 2250.
In the last three years the rice production
has been more or less stable, around 56,000 metric tons.
may be considered as the actual rice production.
So this data
35
3.10
Price Elasticity of Demand for Rice in Nepal
The income elasticity of demand for rice in Nepal is estimated as .3
(FAa 1971).
estimated.
But the price elasticity of demand has not so far been
Basix (1971) and Cummings (1971) have found-that price e1as-
ticity of demand for rice in Pakistan and Bangladesh are -.529 and -.1805,
respectively.
bars of Nepal.
These figures are not available for the immediate neighIt has been found that the price elasticity of demand of
rice for a group of Asian countries lies around -.3. 11
Based on the available information, economists have made a
guess that the price elasticity of demand for rice in Nepal should lie
somewhere between -.2 and -.4.
3.11
Helfare·Loss and Net Benefit-Cost Ratio
'Dueto'Improvemerit in Precision
Assuming the inventory adjustment model, the welfare loss due to
under or overestimation of crop production by 5 percent and 1 percent
error is presented in Table 19.
Due to improvement in precision, there
is considerable reduction in welfare loss.
Other than the various undesirable impacts on the economy, the net
welfare loss due to 5 percent overestimation or underestimation amounts
to 787 thousand rupees.
Other things remaining the same, if the statis-
tical organization takes adequate sample to improve the" margin of error,
Country
Malaysia
Phi1lipines
Japan
Price elasticity of demand
-0.3
-0.3
-0.2
Source
Clew (1971)
Nasal (1971)
Akino & Hayami (1975)
Table 18.
Margin of
error e:
Net welfare loss assessment at different levels of statistical precision and
price elasticities of demand
Price(p)Rs
Quantity (q)Mt
Hi h
tow elasticit
.05
2250
56000
787,500
1050.000
1575,000
.01
2250
56000
Differences
31,500
756,000
42,000
1008,000
63,000
1512,000
High, medium and low elasticity refer to absolute values of a = -.4, -.3 and -.2, respectively.
w
'"
e
e
e
37
the net welfare loss can be dramatically reduced.
The table illustrates
the amount of net welfare loss when the margin of error is leveled at
one percent.
The result is highly encouraging.
The production adjustment model assumes the situation in which producers tend to adjust output along their supply schedules in response to
their price expectation.
As far as the rice crop is concerned, the
situation described in the model is hardly applicable to the Kathmandu
Valley.
Since land in the hilly region is the limiting factor, much of
the rice is produced and domestically consumed by farm families.
Farmers
are unaware of price changes in the grain market, and they are not sensitive to price changes, mainly because they have either no or meager amounts
of rice to sell.
Thus the production adjustment model need not be pur-
sued further.
The difference in the amount of loss due to improvement in the precision is 756,000.
In order to achieve 1 percent precision, the sample
size should be large, which increases survey cost.
Given the area
segment size, 60 hectares, the sample sizes required to meet 5 and 1
percent coefficient of variation are 124 and 554, respectively.
This
is referred to in Table 8.
Table 19.
Measurement of survey cost to improve precision level (from
5 percent to 1 percent) in a 60 hectare area segment of
Kathmandu Valley
Precision level
Survey cost
---..
Fixed costa
Variable cost b
Total
e:
=
.05
6,000
16,610
22,610
e:
=
.01
8,000
74,208
82,208
aaverhead calculation sheet in the appendix.
bVariable cost per unit sample for surveying 60 ha. area segment is
8.93 mandays. Detail workout sheet is given in the appendix.
38
Table 20.
Benefit cost ratio
E1asticit
(Rs
Net benefit
cost ratio
756,000
59598
12.68
Medium
1008,000
59598
16.91
Low
1512,000
59590
25.37
High
Additional cost for 4 percent improvement in the level of precision
comes to about Rs 59,598.
Rs 756,000.
This amount of reduction in welfare loss is
So by simple argument, it is stated that every rupee spent
on improving the marginal degree of precision can save roughly Rs 12.68.
39
4. AERIAL PHOTOGRAPHIC APPROACH
4.1
Collecting Agricultural Statistics
The data to be obtained will be primarily area in crop and crop
yield statistics by using a sampling frame based on aerial photographs
and minor use of topographic maps.
This is an alternative approach to
other methods which might be considered.
was flown in 1965/66.
The aerial photography survey
In the course of the time the total cultivated
land area and land use subarea have changed considerably.
divided into hills and terai (plain area).
Nepal can be
The magnitude of cultivated
land has increased to a large extent, particularly in terai or plains
area.
This impact results from the Malaria Eradication program assisted
by the U. S. in the 1960's, and from the resettlement program of His
Majesty's Government (HMG) Nepal.
In the hills, change isn't very notice-
able.
4.2
Comparison of Two TyPes of Area Frame Materials
(1) Aerial photographs and cadastral information are both at least a
decade old.
Aerial photographs furnish detailed information and they
cover the entire country.
Land survey hasn't covered many areas which
are cultivated because the forest department declares these as forests.
Public-owned land, likewise, was not surveyed.
(2) Area measurement in the cadastral survey is more accurate than
that derived from an aerial photograph.
(3) Aerial photographs can be updated by using satellite imagery to
identify areas with major changes in land cover.
40
(4) Cadastral surveys in some hilly districts are recently completed.
Population pressure on land in the hills is still considerably higher than
in the plains, so increases will be minor.
(5) In hills, an area frame constructed from the cadastral survey
seems to be more appropriate than one based on aerial photography.
The
cost, time, and inaccuracy of measurement factors are believed to be
larger in the case of the aerial photography approach in hills.
(6) In plain area, field sizes are larger than in the hills.
It is
easier to divide the land into count units (i.e., clusters of segments)
and area
segments~
These areas have more roads and easier access.
The
aerial photography technique may profitably be used in this region.
(7) If cadastral survey information is used for the construction of
an area frame, then the undercoverage error in this method, due to incompleteness, will be much higher than the aerial photograph approach.
4.3
Updating of Aerial Photography
The aerial photography of Nepal is a decade old.
So it can't be
efficiently used in areas of major change without updating the photograph.
The updating process is done by superimposing the Earth's Resources
Technology Satellite (ERTS) imagery on the aerial photograph.
The
National Aeronautics and Space Administration (NASA) or the U. S.
Department of Agriculture (USDA) can arrange to get imagery of Nepal.
The scale of 9" x 9" photograph is approximately 1:1000,000.
can be enlarged to a scale of approximately 1:260,000.
The photos
By super-
imposition of this enlargement on the same scale of aerial photograph
41
or topographic map we can transfer the newly cultivated and expanded area
or permanent fallow land, etc.
Similarly, important roads, rivers and
other national features can be transferred on the map for reference.
The enlarged black and white pictures are satisfactory to identify
cultivated land if there is good contrast in the vegetative cover of the
land.
An enlarged and colored photograph of California convinced me that
the total cultivated land can be classified into temporary fallow and
crop land.
These ERTS photos should produce excellent results if imagery
and enlarged photographs can be made available for Nepal.
Plans to in-
stall a receiving station in New-Delhi (India) is in process.
If this
station is established, coverage of Nepal will be more readily available.
Currently, the imagery must be ordered from Sioux Falls, South Dakota,
USA.
4.4
Construction of Area Frame
The basic objective is to estimate the production of a crop (say
rice) which is a function of area under the crop and yield rate.
To
estimate area under crop, we need to classify the total land into cultivated and non-cultivated land.
In this process.we may also do some
additional work to find the land utilization statistics, which are very
important for development planning.
4.4.1
Photo Index
This is the composite photo with the identification number of a
collection of adjacent aerial photographs.
The photo index sheet is
very helpful to locate a particular area of a district or county.
The
identification number in the photo index is specified if an enlarged
photo is required.
42
The photo index sheet represents a district but it cannot be used to
measure the area accurately because of the scale.
For accurate measure-
ment, the district boundaries are transferred to the topographic map of
scale, 1" = 1 sq. km. and the area is measured on the map.
4.5
Stratification
With the help of the updated aerial photographs, the total cultivated
land of a district can be stratified on the basis of its appearance into
the following categories:
Strata
I.
II.
III.
IV.
V.
80 percent or more cultivated land
50 to 80 percent or more cultivated land
20 to 50 percent cultivated land
Less than 20 percent cultivated land
Large lakes, ponds and rivers
VI.
Pasture land
VII.
Forest land
VIII.
IX.
Urban area (cities and populated places)
Others (mountains and nonproductive areas)
Strata I, II, III and IV will probably be reduced to two strata if the
scale of the photographs do not permit this much detail.
There are three districts in the Kathmandu Valley.
The stratifi-
cation is first done on the district level and the district_strata are
combined to form strata for the entire valley.
relatively small unit.
The district is a
If district level estimates are required to meet
a specified level of precision, the costs involved will be very great.
For Nepal, it will likely be too expensive for current year crop
43
statistics.
So an estimate, meeting a specific precision for a larger
unit like Kathmandu Valley, is more practical.
Depending upon the impact
or loss due to inaccurate estimate, a precise estimate, 1 percent to 5
percent coefficient of variation (C.V.), for the entire valley will be
less expensive.
The C.V. for the district level estimate will be higher.
If specified precision is needed for a particular district, then some
additional samples may be taken to meet the desired
p~ecision.
To identify the strata boundary easily, colored pencils are used and
a stratum (e.g., I) is entered on the maps and photos.
Strata boundaries
are formed by natural and physical locations such as rivers, mountains,
ridges, highways, etc., which will enclose relatively homogeneous land
cover types.
4.5.1
Construction of Count Units and Sampling Units
The initial job of a mapping statistician is to study the photo index
of a set of panchayats or of a region and stratify the land on the basis
of the stratum definition.
Applying the criteria of stratification lies
entirely on the understanding and trained eye of the mapping statistician,
because there is no other indicator to differentiate between areas
having 45 percent and 55 percent cultivation.
Since it is a personal
judgment, committing an error, in the marginal cases is quite probable.
Of course, such errors may increase variances, but do not cause bias.
4.5.2
Subdivision of Count Units in Area Segment
For sampling, it is essential to divide the total area of a
stratum into a fixed number of identifiable sampling units.
sampling units, in our sense are termed area segments.
These
The process of
splitting the stratum into individual area segments is a time consuming
44
and expensive job.
count units.
One way of accomplishing this is by constructing
A count unit is a specific area of land containing an
assigned number (usually 7 to 11 units) of elementary frame units (called
sampling units).
Each count unit has 7 to 11 area segments, each of size
1 sq. km., approximately.
This artificial subdivision is defined by
drawing a closed boundary over natural physical permanent locations, such
as rivers, roads, mountain ridges, etc. on the aerial photos.
The area
in each count unit is measured (see below) and this area is divided by
the chosen area segment size to derive the number of area segments
(fractional units are rounded to the nearest integer).
4.5.3 Area Measurement of Count Units and Map Materials
The count units are formed in the photo index but reference is also
made to roads, rivers and other features shown on maps.
The area of a
count unit can't be measured too accurately in the photo index, and
therefore the count unit boundaries are transferred from the photo index
to the topographic or highway map of the scale 1"
= 1 sq. km.
The area
of the count unit is then more accurately measured. by counting the squares
on transparent graph paper or measuring with a planimeter.
Normally, the
count units are irregular and aren't perfect squares, so the area is most
accurately measured by the planimeter.
The map service of the U. S. Army, Washington, D. C. has compiled
topographic maps of Nepal.
The scale is 1:250,000.
This is not the
most desirable scale for detailed or measurement work, but does correspond
almost exactly to the enlarged scale of the ERTS photos.
The Department
of Land Survey, HMG Nepal, has updated topographic maps at district
level; topographic maps in 1"
=1
km. can be prepared for our purpose.
45
4.5.4
List Frame of Area Segments
After measuring the area of the count unit in the map, the mapping
statistician has to calculate the number of area segments that can be
assigned to the count unit.
Then the result is recorded in the following
tabular form.
Table 21.
Map
description
Count unit identification sheet, Kathmandu District
Stratum
Count
unit
number
I
0001
I
0002
I
0003
No. of
assigned
(SQ .km.)
S.U. 's
Area
8.5
9.1
10.3
8
Cum
S.U. 's
Paper
strata
IA
9
8
_17
10
27
IB
IA
II
III
4.6
Paper Strata
This is an artificial stratification of the area frame based on an
ordering of the count units in accord with the following information:
(1) Geographic location of count unit in the topographic map so
that count units adjacent in the ordering are adjacent on the
map;
(2) Specific knowledge of the land use, say rice crop area. Field
report of extension people and knowledge of the statistics field
staff are the major sources of this information. The following
table would be an example of the use of irrigation and degree of
cultivation information which might be used to develop criterion
for paper strata.
46
80% cult.
I 50
-
<
75%
I 20 -
<
50%
I<
20%
Nonirrigated
Rainfed irrigation
Irrigated
Surface irrigation
Pump irrigation
Well irrigation
Paper strata are substrata based largely on qualitative information
or informed agricultural specialists knowledge of the population, and
allocation of the sample with regard to their boundaries should lead to
some increase in the precision of the estimate.
4.7
Area Segment
According to the concensus of the workers in frame construction at
USDA, a count unit of about 7 to 11 sq. km. has been found to be ideal
for small size segments of one square kilometer or less.
Area segments
are the actual sampling units so the magnitude of the sampling variance
(of the mean per segment or total area under a certain crop) depends, in
part, upon the variation in the size of the area segments.
Theoretically,
the optimum area segment size is determined by a comparison of sampling
variance for different segment sizes based on pilot studies.
The size of
the segment which gives the minimum variance for fixed cost is chosen
for survey purposes.
4.7.1
Constraints on the Size of Area Segment
To determine the size of the area segment in Kathmandu Valley, in
the absence of pilot studies, one has to consider the following fundamental
constraints:
47
(1) The average size of holding per farm family is <.5 hectare so
one square kilometer may include at least 200 farm parcels or
families. In the U. S. the farm size is relatively large. An
area segment of size one square mile in the U. S. includes only
seven farms on the average, so it is easy to enumerate all of
them. But this approach doesn't seem to be feasible in Nepal.
So, finding a less expensive, less time consuming approach for
the enumeration of area segments in Kathmandu Valley is a
necessity. This becomes pratica1 only when the size of the area
segment is small enough. However, a square kilometer segment
appears to be the smallest possible area segment which can be
identified on the materials available for Nepal because of the
following additional constraints:
(i) An aerial photo can't be magnified beyond the scale
1" = 1 km.
(ii) Small area segments are difficult to delineate in the PI,
since there are very few physical boundaries for identification.
(2) Although the area segment delineated on aerial photos can be no
smaller than one square kilometer it may yet be possible to
further subdivide this at the time of enumeration into a number
(perhaps four) of subareas shown on a sketch map prepared at the
site. By re-randomization only certain subareas may be selected
for detailed enumeration.
4.8
Alternative Sampling Scheme for Selecting Area Segment
Table 21 gives an example of the total number of area segments and
total area for the cultivated strata.
Given the total sample size n,
samples to be drawn from each stratum may be determined by proportional
allocation.
The sample may be drawn by a simple random sampling (SRS) procedure
equivalent to a single stage in selecting segments.
Once random numbers
are drawn the count units, which contain the selected segments for the
sample, become known.
The selected count units, each of size 1 square
kilometer (approximately) are then subdivided into the preassigned number
of area segments.
48
Cultivated area
Strata
50 -
<
80 percent cultivated
x
20 -
<
50 percent cultivated
x
<
Xl
-n = n
X
l
Xl (88)
> 80 percent cultivated
x
20 percent cultivated
x
Sample size
(62.5)
x
2
-n = n
X
2
(35)
x
-3n = n
x
3
4 (10)
n
x
4
-4n = n
x
2
3
I02(A-S. S-5)
1
Figure 1
The above diagram shows a count unit (bearing the identification
number 0 102 with area segment 8.5 sq. kms.).
Using whatever permanent
boundaries can be seen on the photo, the count unit is divided into eight
segments.
A tolerance limit of 25 percent of the size of the segment is
usually permissible for the determination of segment size.
The area segments are always numbered in a serpentine fashion from
a predesignated starting point and the segment corresponding to the
random number is selected for the survey.
If the selected random number
for the segment in count unit #10 was 97 and the cumulated S.U.'s for the
49
preceding count unit in the frame listing was 92, then the selected segment is No. 5(97-92).
Then a magnitude aerial photo of 24" x 24" is
obtained to measure the area segment more accurately and to identify
smaller subdivisions of the area to be covered during the survey enumeration.
4.9
Selection Procedure
Area segments are selected by the procedure of SRS without rep1acemente
Selected segments are identified on the photo index and the photo
is magnified into 24" x 24" size which can be further subdivided into
tracts or farm parcels.
4.9.1
Sample Size
There are basically two methods of determining the sample size
based on the constraint used.
of precision.
That is:
(1) cost, and (2) desired level
In the beginning, the strata variances (of mean or total)
aren't known so one has to use past experience from similar surveys of
the population or by the results of a pilot surveyor, if neither are
available, hypothetical distributions based on some mathematical results.
Once the survey is done, one can compute strata variances and the
cost function which can be used to determine the sample size to meet a
desired level of precision.
This is calculated by the formula below if
a ratio estimator is to be employed:
=
1-f (C
n
yy
+ C
xx
- 2C
~
)
50
Ignoring f.p.c.
n
=
cyy + Cxx
- 2C
(C. V. )
yx
2
= _M..;.•..;;..S..;.•..;.E..;..~
2
(C. v. )
M.S.E. is the mean square error in the analysis of variance table given
in the appendix.
4.10
Collection of Rice Area Statistics in
Selected Area Segment
In Kathmandu Valley, the average size of cultivated land holding is
less than .5 hectare.
So, a square kilometer area may include as many as
250 farms and it is a lengthy job to enumerate all of them.
So, an
enumerator has to take the following steps to collect the land use
statistics.
(1) Determination of area of the selected segment.
(2) Use of cadastral maps covering a part or complete area of the
segment which is available in the land survey department.
(3) Compute
= segment
=
area - cadastral survey of area
magnitude of the area for which the cadastral map isn't
available.
Thus, the segment consists of two parts, one
covered by cadastral maps and one part not covered by
cadastral maps.
(4) The enumerator should visit the field, divide each area into a
number of subsections.
are to be collected.
For each subsection, land use statistics
51
4.11
Estimation Procedures (Rice Area)
= area
Let
of the i
th
sampled segment in the h
= area
under rice in the i
stratum
th
th
stratum
samples segment of the h
th
i=1,2, ••• ,nh
~
= total
Nh ...
area in the h
th
stratum (hectares)
number of population units in the h
th
stratum
h = 1, 2, ••• ,L
L
x
=
I: x
h=l
Y
=
=
h
(estimated total area under rice, separate ratio estimate)
L
I:
h=l
~
i~l Y hi
~
i=l
~i
L
Var(y ) =
r
I:
h=l
n
I:
r
h
Yhi
Y
i=l
= -h
= =-..;=--n
I:x.
i=l
4.11.1
ni
Combined Ratio Estimate
~
52
1
Y =h
n
n
~
i=l
Y
hi
v(y )
c
-
A
Yst
where R = x
st
53
SUBSAMPLING AREA SEGMENTS
5.1
Construction of Area Frame for Two Stage Sampling
Collecting data in the non-Cadestra1ly surveyed portion of the
selected segment is a time consuming, expensive and difficult job.
To
save time and money, it is preferable to sacrifice some degree of precision in order to reduce the amount of field work.
This can be done by
extending the sample design to multistage sampling.
The area segments
(each of approximately one square kilometer) form the first stage sampling
units.
They are selected in accord with the procedure described earlier.
Using "PI", the aerial photograph of the area, which includes the selected
area segment is magnified into 24" x 24" size.
The mapping statistician
now could have a better and closer look into the area segment and will
divide it into four units, each of one-fourth of a square kilometer
approximately.
The subarea segments in statistical terminology are
called second stage or secondary sampling units.
To illustrate the
situation, two sketches are shown below.
Count unit
Selected area segment
Figure 2
The count unit consists of four area segments, the selected segment only
is presented for illustration.
picture of that area segment.
The next sketch represents the magnified
54
Area segment
I
Subarea segment
Figure 3
The subarea segments are numbered in serpentine fashion.
A simple
random sample of size two is drawn from each selection segment.
the sample design is stratified two stage sampling.
Ultimately,
The field work is
carried out exactly in the way described earlier in section 4.10.
The volume of work, in this case is reduced by about fifty percent.
To save even more time and money the selected area segment may be
divided into eight subarea segments from which one takes a subsamp1e
of two units, each of 12.5 ha. approximately.
However, the determination
of 2nd stage units and of sample size needs further study on cost and
variance.
'5~2'Meth6d6fEstimatirtgAreaUnder
Let Yijk be the area under rice of the k
jth area segment in the i th stratum.
the k
~
subarea segment of the j
~
th
Rice
subarea segment of the
The proportion of rice acreage in
area segment in the i
~.
stratum ~s
given by:
r
ijk
= xYijk
where i
= 1,
2, 3, 4
ijk
j = 1,2 ••• n
i
and k = 1,2
55
The average proportion of rice acreage in the i
th
stratum estimated
by
r
2
Z
1
=-i.. 2n
i
k=l
r
ijk
where
1
2
r · = - Z r ijk •
iJ
2 k=l
Finally, the overall proportion of rice acreage may be estimated by:
r ..•
= -1
4
Z -
1
4 i=l n i
~i
Z
j=l
1
2
2
E
k=l
r
ijk
Basically there are three approaches to estimating rice acreage.
5.2.1
Area Segment Approach
Stratum one covers those areas which are less than twenty percent
cultivated.
Since the cultivated areas are thinly distributed, a set
of samples drawn from this stratum may completely miss the cultivated
area if the size of the area segment becomes too small.
To reduce the
chance of occurrence of this situation, it is customary to keep the area
se~ent
comparatively larger than the segment size in other strata.
So the
56
segment size for this situation is taken as 4 sq. km. (400 ha, approximately) which is four times larger than in other strata.
The coverage
in this case becomes large enough to include scattered and isolated areas.
Let the estimated rice acreage of the Kathmandu Valley be denoted
by
y,
then,
y
2
L:
=
r
k=l ijk
=
is the total cultivated area in the i
th
stratum.
Here it should be noted that the total cultivated area in each
stratum should be known.
This population value is obtained either from
area measurement on aerial photography or Cadestral Surveyor Agricultural
Census data.
If we don't know the size of the cultivated area, or it is
too expensive to obtain, alternative methods of estimation are available.
They pose more difficult problems in the computation of estimated
variance because the estimate is the product of two random variables.
The estimate becomes
where Xi" is the estimated rice acreage in the i th stratum.
Estimation of
Area at Stratum Level
th
To estimate the cultivated area of the i
stratum, one can measure
'5~3
CU1ti~ated
the total cultivated area of all count units which include the selected
segments.
We know that there are n
i
samples in the i
th
stratum, so the
57
cultivated area of n
i
count units is available.
number of count units in each stratum.
The area frame supplies the
Therefore the estimated "total
cu1 t i vate d area i n t h e i th stratum i
s ·
g~ven b y t h e f 01 1 owing formula.
X"i
(1)
X cij '
where Xcij is the cultivated area in the count unit that contained the
th
stratum.
selected area segment. C. = number of count units in the i
~
Another method is also based on the cultivation area of count units
which include the selected area segments but also takes account of the
known variation in number of segments assigned each count unit.
X .. be the cultivated area of the count unit of j
th
c~J
segment in the i
th
stratum and also let n
Let
selected area
be the number of area
cij
segments in the count unit, then the estimated area of the i
th
stratum
is estimated by the following expression.
'"
X"i
= (number
=
of area segments)
sum of the areas in count
units containing selected
area segments
sum of the number of area
segments included in count
units
._-------
5.4
Estimation of Sample Variance
A final approach is based on average cultivated area.perunit area
segment in the count unit.
Let X i' be the cultivated area of the count
c J
th
th
unit, having j
selected area segment in the i
stratum.
58
Let n
cij
be the number of area segments in the count unit then
X
cij
n
N
i
i
Xlii =n- E
i j=l
= Xcij
n
cij
X
cij
n
cij
where N is
i
the number of area segments in the i
th
stratum.
Among these different
estimators the second and-third ones seem to yield
variances ~
compar~tively
smaller
AIl a,l.ternative estimate of the same characteristic y (the
acreage under rice) is given by
ni
4
A
Y
=
2
E Yijk
E
j=l k=l
i=l n i 2
E
E
E x
j=l k=l ijk
2
E Y
is the sum of rice acreage over all the samples of
ijk
kl=1
where
the i
th
stratum.
2
E
k=1
x
ijk
is the sum of the cultivated areas over all the se-
1ected samples (i.e., 1st and 2nd stage sampling units) in the i
Xi
=
the total cultivated area of the i
5.5
th
v(y)
=
=
4
E
i=l
2
Xi
veri ..)
stratum.
stratum and this is known.
Estimate of Sample Variance
"
The estimated variance of Y
is given by:
th
59
A
where Y is calculated as X
cij • rij./nCij'
ij
In this form we can use
10
Cochran's formula 10.16 to approximate its variance:
5.6
Illustration with Hypothetical Problem
To illustrate the application of the theory of two stage sampling,
a hypothetical numerical example has been fully worked out.
Statement of the Problem
To estimate the total rice acreage, a sample survey was carried out
in a certain region.
Using intensity of cultivation as a stratification
variable, the region was divided into 4 strata.
From each stratum, a
sample of area segments was selected without replacement.
Each selected
segment was divided into four secondary sampling units of approximately
equal size.
A random sample of subarea segments of size two was drawn
from each selected area segment.
Data collected from the survey and addi-
tiona1 information on total cultivated acreage at stratum level is presented in the following table.
The between segment variances for each of the strata are given by
the formula:
s
2
rio •
.-1
n -1
i
and from the data they can be computed as:
s
2
rl. .
10
1
= 3.-1
(.0050 + .0006 + .0022)
Cochran, op cit., p. 278
=
.0039,
60
where
2
s
,rij.
=
The computational form of estimated variance of y is given, by the following
expression:
v(y)
=
4
2 + 4
1
X2 {(L _ L) sri
L -NNi
i n
i=l n i i
i=l
i
L
1
4
2
Sij }.
In this formula, we assume that ~i's are known.
In a typical situation, when Xi's are not known, then they are
estimated from the samples.
y =
Then:
4
L Xi 1:i"
i=l
which is a linear function of the product of two random variables,
The determination of sample variance for products becomes a little
complicated, but it is possible to view Xi
to N times the average:
i
ri
as approximately equal
e
e
Table 22.
e
Observation in hectares of rice (y) and total cultivated land (x) for 30 subarea segments in
a hypothetical sample survey
Strata
N
i
n
i
1-
<20 percent cultivation
40
3
2.
20-30 percent cultivation
60
4
3.
50-<80 percent cultivation
40
4
4.
80 percent and above
30
4
Total cult.
1
area of the
strata (ha) x iik
81
15.500
77
30
5.800
20
22
3.800
28
27
3.500
25
Segment
I Yiik
27
14
10
8
10
12
18
19
2
x iik
80
100
25
30
25
25
20
30
I Yiik
10
20
10
10
10
13
14
18
4
3
x
iik
85
92
25
20
30
20
26
28
Yiik
9
16
9
8
11
8
18
18
x iik
--
-26
24
23
25
24
22
I Yiik
--
-11
10
10
10
18
16
0I-'
Table 23.
Computation sheet for the estimation of area under rice
Strata
1.
<
20
percent
Area
segment
size
(ha)
Total cultivated
area of
the stratum
Observation of selected subarea segments
N
i
n
i
81
370
77
410
cultivation
15,500
40
3
420
2.
20 to
95
50 percent
105
5,800
60
4
cultivation
90
100
3.
50 to
Cultivated Area under
area x
rice Yijk
iik
100
80 percent 110
cultivation
<
90
100
3,800
40
4
80
100
85
92
30
20
25
30
25
20
26
24
22
28
25
25
30
20
23
25
27
14
10
20
9
16
10
8
10
10
9
8
11
10
10
12
10
13
11
8
10
10
r
2
Y
ij k
= .::..!ik - =!.
x
r ij 2
ij k
•
r Yi · k
k=l
2
r
J
x
k=l ijk
.3333
.1818
.1250
.2000
.. 1053
.1739
.3333
.4000
.4000
.3333
.3600
.4000
.4231
.4167
.4545
.4286
.4000
.5200
.3667
.4000
.4348
.4000
.:
ri
1
=-
n
i-
r r
.. n i j =1 ij
.2576
.1625
.1865
.1396
(.2110)
.3667
.3667
.3834
.3800
(.3800)
.4199
.4416
.4600
.3834
.4256
.4174
(.4242)
0\
N
e
e·
e
e
e
e
Table 23 (continued)
Strata
4.
80 per-
Area
segment
size
(ha)
Total cultivated
area of
the stratum
Observation of se1ected subarea segments
N
i
°i
100
cent and
above
90
110
100
3,500
30
4
Cultivated Area under
area x
rice Y
iik
iik
27
25
20
30
26
28
24
22
18
19
14
18
18
18
18
16
2
ni
Y
1 k~lYijk 1
r
=~ r
L r
r =2
ij
ijk
x
i..
n
j=l
ij·
i
ijk
.L x
ijk
1<:=1
A
:=2
.6667
.7600
.7000
.6000
.6923
.6429
.7500
- .7273
.7134
.6's00
.6676
.6924
(.6814)
.7387
*Figure in the parentheses indicates the proportion of rice acreage to the cultivation area based
on all samples in the i th stratum.
0W
64
Estimation of Sample Variance
4
2
_
L Xi v(r i )
••
=
i=l
n
=
4
L
i=l
1
2112
X {(---) 8
i
ni
Ni
rio.
+-.-
i
112
(-.---)8
L
n i Ni j=l
s
mij
Mij
2
r2 ..
1
1
2
2 1
1
+ X2 (- - - ) s
- - ) s2
+ X3 (tr.:
4 n 4 N4
3 N3
r3 ..
r4· .
2
X
2
+_1_ 1
n N 4" (sll. +
1 1
2
X __
+ _4
n4N4
=
8
2
41 • +
8
8
2
12 . +
2
42 . +
4
8
8
2
13 .)
2
2
43 . + s44.
(15 t 500)2
(5800)2
56
x 37 x .0039 +
4
x 60 x .0006
3 x 40
+
(3800)2 x 36
(3500)2 x 26
4 x 40
x .0011 +
4 x 30
x .0016
+
(15 t 500)2
(5800)2
3 x 40
x .0042 + 4 x 60 x .0013
+
(3800)2
(3500)2
4 x 40 x .0022 + 4 x 30 x .0027
A
S.E. (y) = 557.22
= 310495.93
ij.
}
65
2
s r2 •• = .0006
2
s 3
r
s
••
2
r4 ••
= .0011, and
= .0016.
th
.
.
...
Th e sub area var1ance
wi t h·1n t h e i
stratum j t h
segment
is given
by
the following expression:
The following table presents the variances between ratios (due to
subarea segment) within each of the strata.
Tabla 24.
Variation between ratios of subarea segments within the strata
Stratum
averages
Strata
5
2
.0024
13 .=
2
2
s2l. = .0022, s22.= .0022,
5
2
23 .= .0008,
33
2
s3l. • .0003,
5
2
.0072 ,
32 .=
5
4
2
s4l. • .0044,
5
2
• =.• 0050,
42
1
2
sll.= .0115,
2
5
2
.0028,
12 .=
8
.0056
2
5 24 .=
0
.0013
2
2
.0006, s34.= .0006
33 . -
.0022
2
2
= .0012, s44.= .0003
43 •
.0027
66
5.7
1.
Estimation of Total Area Under Rice
The area under rice is estimated by the following formula:
y"
=
4
L:
i=l
Xi
r
i..
= 15.500 x .1865 + 5800 x .3834 + 3800 x .4256
+ 3500 x .6929
= 9156 • 9000 ha.
Confidence Interval
Assuming normality condition, the effective d.f. (due to Satterthwaite,
11
(1946), see Cochran· ) in stratified sampling is given by
= 4.8678
where
g =
h
11
Nh(Nh - ~)
~
gl
=
40(37)
3
=
493.33
g2
=
60x56
4
=
840
g3 =
40x36
4
=
360
g
30x26
4
= 195
4
Cochran, op. cit. , pp. 94 and 95.
=
e
67
/
2 4
gh s11
Stratum
gh
2
sh
2
8h sh
2 4
gh s.n
1
2
493.33
.0039
1. 9240
3.7018
1. 8509
840.00
.0006
0.5040
.2540
.0847
3
360.00
.0011
0.3960
.1568
.0523
4
195.00
.0016
0.3120
3.1360
.0973
.0324
2.0203
~-1
Thus the degree." of freedom for t is taken as .5, and
2.571.
=
t. 05 (5
Thus the confidence interval is given by:
y - t
.05,5
12
Is- ~
9164.1200 - 2.571 x
2.
77 31; 5032
.
557~221~<
1432~6168 <
9164.1200 i.e.,
A
y ~ y + t 05 , 5
<Y
<
Y
<
9164.1200 + 2.571 x 557.2216
Y < 9164.1200 + 1432.6168
10596_.7368 •
The next alternative estimate for the total area under rice is
ni 2
L:
L: Y
4 j=l K=l ijK
A
y
=
i=l
-
ni
2
L:
L:
•
Xi
x
j=l K=l
ijK
= .2110 x 15,500 + .3800 x 5800 + .4242 x 3800
+ .6814 x 3500
=
9471 • 36 ha.
68
6. SUMMARY AND CONCLUSIONS
This work is an effort to describe and illustrate suitable methods
for collecting agricultural crop statistics in Nepal.
Methods based on
the cadastral survey, and on aerial photography are somewhat different,
yet both obey the fundamental principles of area sampling.
An area frame
based on aerial photography possess the qualities of completeness, no
ambiguity, free from duplication, etc.
With the help of current satellite
imagery, the updated photos could be used efficiently.
Technical manpower
and ground map materials are the limiting factors in adopting the technique.
The cost factor can be dramatically reduced by using multistage sampling.
On the whole, the aerial photographic approach may be comparatively better
than the frame, based on Gadastral survey information and could be profitably used in the plane area of the country.
The Cadastral survey in hilly districts is still in progress.
Where
it has been recently completed, a frame based on Cadastral survey and
materials would work pretty well.
However, for those hilly districts
in which the survey was completed quite a long time ago, the survey
information should be updated in close collaboration with the land administration, land survey and agricultural extension department.
Cultivated land, particularly. in plane areas, has changed in land
use to a large extent and thus the frame will suffer an increase of
variance due to poor control of the amount of cultivated land in each
segment.
Cadastral survey materials should be sufficiently improved
before they are used in the plane land.
Until now, Nepal seems to have preferred to publish crop production
statistics at the district level.
A district as such is a relatively
69
small administrative unit.
Since the sample size required for meeting
a given specific precision does not depend very much on the size of the
population, collecting agricultural statistics for each of these units
would be pretty expensive.
If from an administrative point of view a
population consisting of geographically contiguous districts (4 or 5 of
them) is sufficiently internally homogeneous to be dealt with as a
unit, then it is much less expensive to furnish estimates for this entire
unit than for each district.
Suppose an estimate with 5 percent coefficient of variation is called
"adequate" as seems reasonable for most administrative purposes.
It
would require a sample size roughly 3 or 4 times as large to provide
adequate estimates for say four separate districts as to provide an
adequate estimate for the combined area of the four districts.
From planning considerations, Nepal has been divided into four
development regions.
To increase the efficiency of current agricultural
statistics system and also to reduce cost dramatically, it is believed
that crop production statistics, satisfying the desired level of precision for hills (including mountains) and terai (including inner terai),
within each development region (eight areas in all), may be more appropriate than statistics for 75 separate districts;
The actual survey procedure will likely not be restricted to a
single crop.
Thus, the methods of this thesis will need to be applied
to other agricultural crops than rice.
For specific crops such as
sugarcane or cardamon or jute, etc. the population or geographic area
has to be redefined on the basis of available information.
cation in population size, area
desirable.
s~gment
Some modifi-
size, sample size, etc. may be
70
7. LIST OF REFERENCES
Cochran, W. G.
New York.
1963.
Sampling Techniques.
Des Raj. 1968. Sampling Theory, India.
Company, Ltd.
John Wiley and Sons,
Tata McGraw Hill Publishing
Economic Analysis and Planning Division. 1972. Agricultural Statistics
of Nepal, Kathmandu, Ministry of Food and Agriculture, HMG Nepal.
Gurung, Harka. 1970. Nepal: A Profile.
Applied Economic Research.
HMG Press, Nepal Council of
Houseman, Earl E. 1975. Area frame sampling in agriculture.
Reporting Service, Washington, D. C.
Statistical
Huddleson, Harold F. 1976. A training course in sampling concepts for
agricultural surveys, SRS, USDA, Washington, D. C.
Huddleson, Harold F. and Clarence Dunkerley. 1974. A methodological
report on agricultural statistics in the Dominican Republic.
Dominica1 Republic, U. S. Aid Mission.
National Planning Commission.
HMG.
1975.
The fifth plan (1975-1980).
Nepal,
Statistical Reporting Service. 1974. Tunisian Acreage and Livestock
Enumerator Survey, Vol. I and II. USDA, Washington, D. C.
Sturdivant, Tyler R. 1971. Draft report on establishment of yield and
area benchmarks for paddy, maize and wheat in five selected districts
of Nepal. Kathmandu, U. S. Aid Mission.
Sukhatme, P. V. and B. V. Sukhatme.
1970.
India.
Asia Publishing House.
Yujiro, Hayami and Willis Peterson. 1972. Social returns to public
information services. Statistical Reporting of U. S. Farm Commodities.
American Economic Review, Vol. LXII, No.1, JASA.
Zarkovich, S. S. 1965. Estimation of areas in agricultural statistics!
Rome Food and Agriculture Organization of the United Nations,
•
72
8.1 Selected Area Segments (40 ha. size)
Kathmandu District
Obs.
1
Parts
SEL
1
556
30
02303
02502
1
7
1
1
2
556
30
08302
08701
1
45
1
2
83402
83501
1
554
..
30
556
30
130
1
Obs., PN and SN have usual meaning.
2The first selected sample includes subarea segment from 02303 to 02502
inclusive.
~1 of the first observation means the selection sample has its seventh
position, the serial order arrangement of sampling units in the population.
4
SEL means selection segment.
5ARS serial order of selected area segment.
This is a model copy of computer reprint. Corresponding to each
district of the Kathmandu Valley similar reprints for 40, 60 and 80 hectare
area segments are available.
4It
73
8.2 Sample Data for Variance Comparisons
Kathmandu District
Sample
no.
Code1
no.
Area segment size
40 hectares
Cu1tiArea
vated
under
area
rice
(x)
(y)
Area segment size
60 hectares
Cu1tiArea
under
vated
area
rice
(x)
Area segment size
80 hectares
Area
Cultiunder
vated
area
rice
(y)
(x)
(v)
12
02303 to
35.62
02502
08302 to
08701
32.83
03901 to
04102
52.81
04501 to
04503
48.25
05701 to
05801
34.80
07101 to
07103
43.25
08908 to
09201
40.46
09202 to
09302
43.50
09402 to
09504
41.54
10206 to
10305
54.85
12902 to
13102
44.74
13701 to
13701
50.90
13
13903 to
13903
44.32
27.86
58.33
29.95
080.41
44.47
14
17612 to
17705
47.16
44.66
62.03
50.66
092.71
73.83
15
18181 to
18105
41.58
11.11
96.20
28.68
107.26
34.41
16
18902 to
19202
36.13
18.77
62.26
25.51
068.10
37.37
1
2
3
4
5
6
7
8
9
10
11
12.52
60.98
23.67
070.47
25.94
11.64
60.18
25.33
072.91
37.10
40.02
74.32
51.99
096.69
62.96
09.63
59.45
15.08
079.08
20.54
16.90
55.50
29.49
078.19
47.28
32.79
55.35
34.53
081.22
55.41
32.58
61.19
51. 76
071.35
58.70
28.48
62.46
37.24
082.11
56.72
34.46
51.25
36.02
085.04
63.31
40.30
65.29
40.66
083.62
58.82
31.17
63.04
45.68
088.75
69.76
42.04
58.45
45.98
096.34
65.73
74
Kathmandu District (continued)
Sample Code
no.
no.
1
Area segment size
40 hectares
Area
Cu1tivated
under
area
rice
(y)
(x)
Area segment size
60 hectares
CultiArea
vated
under
area
rice
(y)
(x)
Area segment size
80 hectares
Cu1tiArea
under
vated
area
rice
(v)
(x)
17
46801 to
41.06
46805
37.06
56.67
41.04
074.04
59.34
18
49911 to
37.56
50201
18.84
62.03
34.50
078.65
38.08
19
50803 to
45.65
50901
31.66
64.75
46.79
073.64
49.34
20
53801 to
48.14
54201
33.18
54.05
30.08
083.31
54.90
13.90
63.15
34.31
068.47
33.54
36.31
32.49
24.84
080.77
53.96
22
54301 to
36.05
54501
54801 to
48.48
54903
23
64403 to
26.80
64404
07.70
63.04
17.41
073.10
20.14
24
67811 to
49.78
67815
32.38
69.79
46.09
069.79
46.09
25
69401 to
45. 8 7
69502
23.25
58.48
38/69
069.34
40.13
26
79703 to
37.26
70801
31.14
53.02
44.94
076.09
51.30
27
75203 to
29.56
75301
18.64
55.85
40.16
089.88
75.60
28
76101 to
38.10
76302
34.46
38.10
34.46
098.78
75.42
29
80803 to
38.52
80901
28.60
54.20
47.81
082.98
63.21
30
83402 to
41.15
83501
36.78
60.36
53.15
084.80
79.15
21
1
For each sample. the first and last code number of area segment is
specified. The codes are illustrated in the beginning of 40 hectare segments.
To make the variances comparable, 80 hectare segments include more or less
all of 60 hectare segments which ultimately consists of all or the major part
of 40 hectare segment area •.
e
75
La1itpur District
Sample
no.
1
Area segment size
40 he tares
Cu1tiArea
vated
under
rice
area
(v)
(x)
Area segment size
60 hectares
Area
Cu1tivated
under
area
rice
(x)
(y)
38.48
13.33
54.20
17.62
2
22.31
05.79
54.62
3
4
49.01
24.93
47.58
5
40.39
6
7
28.93
30.07
08.08
20.50
36.26
8
37.34
9
10
Area segment size
80 hectares
CultiArea
vated
under
area
rice
(x)
(v)
19.49
75.65
66.21
27.78
29.96
47.26
29.17
71.00
32.23
80.43
58.73
56.00
14.10
80.43
83.99
52.72
41.41
81.33
56.00
16.80
51.41
48.49
58.71
65.10
32.54
40.52
38.73
36.61
30.01
23.92
28.47
52.46
77.77
87.52
87.91
40.33
59.48
64.61
08.05
20.78
39.26
11.52
13.81
23.17
78.95
11
56.43
44.64
84.54
12
22.36
04.47
65.82
29.24
78.40
32.73
37.75
13
49.30
14
35.56
93.85
59.07
53.76
11.80
40.35
59.57
36.78
93.85
78.75
80.61
53.76
18.11
15
23.35
07.09
26.42
16
37.31
55.74
44.16
40.70
41.97
20.16
13.04
85.34
17
18
19
11.80
08.78
24.08
27.63
18.64
08.83
20
21
47.06
45.65
36.64
38.06
55.96
57.75
22
68.01
23
37.26
24
54.39
61.92
53.65
39.90
77 .67
85.32
13.82
82.24
82.74
54.92
34.56
47.58
86.05
21.95
52.15
65.54
35.39
52.42
38.79
46.73
16.29
13.19
52.53
50.32
66.07
32.14
23.68
26.69
78.24
82.08
90.64
47.53
31.28
35.08
10.48
20.70
56.70
52.79
30.48
16.70
82.82
74.70
27
28
42.40
10.27
48.42
12.72
79.24
36.77
22.03
18.28
36.78
64.16
19.79
81. 71
24.15
29
35.47
07.40
07.13
56.72
11.59
16.91
30
38.94
08.39
58.46
14.12
83.59
74.20
25
26
56.17
17.92
76
Bhaktapur District
Sample
no.
Area segment size
40 hectares
Area
Cu1tiunder
vated
rice
area
(y)
(x)
Area segment size
60 hectares
Area
Cu1tivated
under
area
rice
(y)
(x)
Area segment size
80 hectares
CultiArea
vated
under
area
rice
(y)
(x)
1
068.89
045.63
68.88
45.63
090.32
64.40
2
." 3
066.34
054.82
66.53
46.83
080.97
57.12
025.61
021.71
45.84
38.58
093.19
71.40
4
024.88
014.23
59.46
31.27
085.32
42.27
5
032.10
025.50
48.38
36.96
074.58
55.44
6
045.60
027.15
68.02
50.71
068.04
47.82
7
036.23
022.84
71.95
49.08
083.79
56.84
8
043.60
015.25
58.37
33.55
091.15
57.72
9
064.69
58.93
29.98
78.87
012.28
64.69
52.20
092.71
10
058.94
003.67
086.59
41.23
11
050.92
044.03
54.17
41.56
082.65
64.69
"
12
048.82
041. 78
59.30
56.55
108.12
99.25
13
053.50
044.52
42.46
36 •.41
101.22
63.41
14
036.79
015.76
84.97
54.42
087.08
62.61
15
039.08
026.00
58.23
38.68
061.65
40.52
16
052.49
027.31
65.00
41.24
079.38
47.17
17
052.37
027.45
59.38
33.76
096.74
36.08
18
027.19
019.21
55.62
29.76
069.34
55.31
19
054.36
032.94
54.35
43.50
077.73
63.90
20
036.38
025.43
44.62
31.30
077 .62
59.53
e
8.3
JHstrict
1. Kathmandu
2. Lalitpur
Variable
Summary Statistics for Variance Comparisons
40 ha. segment
.1 Vari- I S.E. .1
Mean ance
of mean C.V.
60 ha. se ment
VariS.E'I
Mean ance
of mean C.V.
I
80 ha. segment
VariS.E.,
Mean ance
of mean C.V.
I
I
X
41.89
45.43
1.23
16.09
59.74
110.99
1.92
17.63
81.21
98.90
1.81
12.24
y
27.29 114.98
1.95
39.28
36.88
108.78
1.90
28.27
51. 71 262.69
2.95
31.34
R
0.63
0.04
0.03
32.63
0.63
0.03
0.03
29.27
0.63
0.02
0.03
26.65
X
40.15
73.98
1.57
21.41
58.21
93.28
1. 76
16.59
81.11
32.09
1.03
6.98
y
17.82 123.86
2.03
62.43
27.63
183.76
2.47
49.06
36.24 252.07
2.89
43.80
0.05
0.04
52.36
0.47
0.04
0.03
42.97
0.03
0.03
40.85
X
43.04 231. 32
3.48
35.33
59.12
106.11
2.30
17.42
84.40 130.35
2.55
13.52
y
29.53 217.68
3.38
49.94
41.43
81.80
2.02
21.82
58.27 212.63
3.26
25.02
0.03
0.04
27.30
0.70
0.01
0.02
17.54
.02
19.17
R
3. Bhak.tapur
e
e
R
0.43
0.66
0.44
0.69
0.01
2
Mean square error S
Area segment
Area segment
Area segment
80 ha.
60 ha.
40 ha.
1. Kathmandu
71. 9628
134.1435
159.8348
2. La1itpur
86.9780
138.7355
223.6257
3. Bhaktapur
57.6129
50.0406
150.2257
.......
.......
8.4
Analysis of variance of rice land (Y) as a proportion of the cultivated land (X) for a 60 hectare
area segment (optimum size), for the districts of Kathmandu, La1itpur, and Bhaktapur, respectively.
Source
I
D.F.
I
Sum of squares
I
Mean square
I
F value
298.75
I
I
R-square
0.0001
0.911519
PR > F
I C.v.
Kathmandu District:
Model
1
40076.01110001
40076.01110001
Error
29
3890.16429999
134.14359655
Uncorrected total
30
43966.17540000
Model
1
24210.03401474
24210.03401474
Error
29
4023.33168526
138.73557535
Uncorrected total
30
28233.36570000
Model
1
34925.51766277
34925.51766277
Error
19
965.97313723
50.84069143
Uncorrected total
20
35891.49080000
31.4018
Std. dev.
Y mean
11.58203767
36.88333333
La1itpur District:
174.50
0.-0001
0.857497
Std. dev.
11. 77860668
42.6282
Y mean
36.88333333
Bhaktapur District:
686.96
0.0001
Std.dev.
7.13027587
0.973086
17.2083
Y mean
41.43500000
......
00
e
e
e
79
8.5 Survey Costs
Overhead Cost Assessment (for 40, 60 and 80 hectare segments)
~o~t
1.
Staff
(a) Statistician
(b) Asst. statistician
(c) J~ior administrator
7,800
4,800
3,000
2.
Office equipment
700
3.
Stationary and office materials
500
4.
Supervision
5.
Miscellaneous
It should be noted that
area segment.
(Rs)
1,000
200
18,000
ove~head
cost does not change by size of
When the sample size exceeds 300 or so, then it becomes
pretty difficult to manage the field supervisory work with the initial
number of staff and office materials.
The change is of course due to
change in sample size but a small change such as 40 or 50 additional
samples does not incur -the additional cost.
In
Ch~Pter
3, sample size
to improve precision-went up to 554, so overhead cost has been slightly
inflated.
Some Assumptions in the Construction of Cost Functions
(1) The fixed cost covers a complete fiscal year.
The crop surveys
are conducted usually three times a year so that all important seasonal
crops are covered.
The survey conducted in late summer season covers
other contemporary rice crops and it is a hard job to isolate the cost
incurred to cover the rice crop only.
So it is assumed that the rice
crop survey shares about one-third of the total fixed cost.
80
(2) Map materials last for longer periods and it could have been included in the fixed cost.
Since the required number of map materials
vary according to the sample size, it has been included in the variable
cost.
(3) Salary and other costs refer to the second half of the year 1976.
(4) Using knowledge of previous agricultural survey, the initial
cost has been expressed in mandays.
One manday is equivalent to 8 working
hours and cost for one manday equals Rs 15/= at present.
81
8.6 Variable Cost Assessment for 40, 60 and 80
Hectare Area Segment
Variable cost assessment
(a) Materials
(1) Maps (area segments 2.5)
(2) Forms
(3) Writing materials
(b) Sampling
(1) Writing address (preparation of
area segments, sample selection
and identification)
(2) Field organization & work load
(c) Traveling
(1) Visiting the location and comeback
(2) Within the area segment
(d) Field operation
(1) Contact panchayat people & ward members
(2) Preparation of the list of cultivators,
area of the parcel
(3) Identification of subsection on map and
also on ground and record observations
(e) Survey for net harvested area
(f) Data processing & estimation
(1) Totaling of area in the field
(2) Processing & estimation
(g) Miscellaneous
Mandays for sample of hectares
40
60
80
(2.35)
(3.10)
(1. 50)
1.23
.17
.10
2.00
.25
.10
2.65
.30
.15
(.20)
(.30)
(.30)
.15
.05
.23
.07
.23
.07
(1.00)
.50
.50
(1.10)
.50
.60
(1. 30)
.55
(2.60)
(3.39)
.50
.50
.50
.65
(4.23)
.60
1.60
2.24
2.88
(.90)
(.90)
( .59)
(1. 00)
( .50)
.20
.30
(.30)
7.00
.24
.35
(.30)
8.93
.75
.75
(.85)
.40
.45
(.30)
11.08
82
8.7 FOrmation of 40 Heetare Area Segment
Kathmandu District
Cbs.
PN
SN
STCU
ENCU
Parts
N1
1
556
30
01101
01101
1
1
2
556
30
01201
01401
1
2
3
556
30
01501
01601
1
3
556
556
30
83702
83903
1
556
abs. means number of observations.
PN means number of clusters or area segments.
SN means number of samples to be drawn from the population.
STCU means starting or beginning code of the subsection of the area
segment.
ENCU means ending or last code of the subsection of the area segment.
In observation 2, the area segment includes subsection areas from
01201 to 01401 inclusive.
N1 is the number of area segment.
This sheet is a model copy of the computer reprint. Corresponding
to each district of the Kathmandu Valley, similar reprints for 40, 60 and
80 ha. area segments are available.