School of Geography
University of Leeds
GEOG 1230 BA
2003/2004
Level 1/Semester 2
Lecturer: Tim James
Material originally prepared by Dr. Joe Holden
Semester 1 – Week 4
Worksheet 1
Submission Date: Oct 31st, 1200.
Your Name:
Student ID number:
Programme of Study:
Sampling
Figure 1 is a map of the soils around Rhyl, a coastal area of north Wales. The majority of the soils in this
area have been classified into six types, based on the field work and classification of the Soil Survey of
England and Wales. This exercise illustrates some of the problems that will be encountered in any attempt
to obtain and use reliable samples from maps. The first problem may be phrased as ‘What sample size is
necessary to obtain a reliable estimate of the areal coverage of each soil type on the map?’ The second
problem involves the choice of a sampling design: ‘What are the differences in practice between the
results obtained from random sampling and the results obtained from systematic sampling?’
The remainder of the exercise considers the use of sampling to compare maps and to approach the testing
of hypotheses. Figure 2 is a map of the underlying parent materials in the same area as Figure 1, based on
the Drift Geology recorded by the Geological Survey. A subjective appraisal of the two maps suggests
that there is some correspondence between the two sets of patterns. This is turn suggests that the
underlying parent material is an important determinant of soil type in the area mapped. There are,
however, other soil-forming factors – such as relief, organisms (vegetation, animals, humans), climate
and time – which are independent of parent material and may account for some of the pattern of soil types
in Figure 1. It would be of some value therefore, to obtain objective information on the extent to which
particular soil types are associated with particular parent materials. In this way, application of sampling
techniques may be considered the first stage in the testing of a hypothesis by objective procedures.
1. The aim of this section is to draw a random sample of points from Figure 1 using a number of
sample sizes.
a) Construct a grid-reference system along the horizontal and vertical axis of Figure 1. The interval must
be suitable for use with random number tables. Use tracing paper!
b) Using the random number table provided, locate 80 random points on the map (use small black dots).
After the 5th, 10th, 15th , 20th, 25th, 30th, 40th, 50th, 60th, 70th and 80th points have been located,
calculate the percentage areal coverage of the following: Use tracing paper!
i)
Type II
ii)
Type III
iii)
Type IV
iv)
Type V
Note: the total cover of these four soil types may not be 100 % since there are other soils on the map.
Enter the percentage coverage into the table below:
Table 1. Percentage areal cover of four soil types as determined by a range of random sample sizes.
Sample size
5
10
15
20
25
30
40
50
60
70
80
Type II
Type III
Type IV
Type V
c) Draw up a graph of estimated percentage cover (y-axis) against sample size (x-axis) for these four soil
types. Plot all four series on one graph, remembering to label each series. You may stick some graph
paper onto the worksheet in the space below if you wish. Alternatively, you may use Excel or a
similar spreadsheet package. Remember to label your axes properly. You will be penalised if you
don’t.
d) Comment on the form of the graphs and draw conclusions about the necessary sample size for a
representative sample in each case.
2. The aim of this section is to compare samples drawn by means of random and systematic
sampling designs.
a) By means of a grid, locate a systematic sample of points on the map (Figure 1) – use small blue or red
crosses Use tracing paper!
b) As in section 1 enter values of percentage areal coverage for a range of sample sizes in the following
table:
Table 2.Percentage areal cover of four soil types as determined by a range of systematic sample sizes
Sample size
5
10
15
20
25
30
40
50
60
70
80
Type II
Type III
Type IV
Type V
c) Compare the estimated percentage cover of the four soil types obtained by systematic sampling with
the results obtained in Section 1 with a similar sample size. Write down the differences and
similarities of the two datasets.
d) Write your conclusions about the relative suitability of the two alternative sampling designs, bearing
in mind the differences to be expected on theoretical grounds.
3. The aim of this section is to compare the map of soil types with the map of parent materials
(Figure 2).
a) Using either the random or the systematic design, transfer the same 80 points to the parent material
map. State which method you transferred across to the parent material map:
b) Cross-tabulate soil type with parent material. That is, enter the number of points falling in each cell of
the table below – For example, simply count how many of the soil Type V points lie on Type A, Type
B, Type C, Type D, Type E, Type F/G or other parent materials. Complete the whole table:
Table 3. Number of sites where each soil type overlies a given parent material. N = 80.
Parent Material Category
Soil type
Type A
Type B
Type C
Type D
Type E
Type F/G
Type I
Type II
Type III
Type IV
Type V
Type VI
Other
Others
c) Complete a similar cross-tabulation showing the percentage of each soil type within each parent
material category:
Table 4. Proportion of each soil type that is found to overlie a given parent material, %
Parent Material Category
Soil Type
Type A
Type B
Type C
Type D
Type E
Type F/G
Type I
Type II
Type III
Type IV
Type V
Type VI
Other
Others
d) Construct a third cross tabulation showing the percentage of each parent material category that is
associated with particular soil types:
Table 5. Proportion of each parent material that is found beneath a given soil type, %
Parent Material Category
Soil Type
Type A
Type B
Type C
Type D
Type E
Type F/G
Type I
Type II
Type III
Type IV
Type V
Type VI
Other
Others
e) Do the results in the three tables (Tables 3, 4 and 5) support the hypothesis that particular soil types
are characteristic of particular parent materials? Fully justify your answer.
f) Discuss ways in which the results of this study might be improved and the conclusions could be made
more decisive.
Work to be submitted by 12pm on Friday October 31, 2003 either in the lecture or in the
GEOG1230 pigeon-hole in the Basement of the Geography Building.
You must submit this worksheet and the two pieces of tracing paper, stapled together.