University of Leeds / Level 1/Semester 2
GEOG 1230 BSC / 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) gleyed soils
ii) brown earths
iii) calcareous soils
iv) podzolized soils
Note that 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 / 80Gley
Brown Earth
Calcareous
Pozdol
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 / 80Gley
Brown Earth
Calcareous
Pozdol
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 podzol points lie on alluvium, till, glacial, limestone, peat, sandstone 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 CategorySoil Type / Alluvium / Glacial till / Fluvial-Glacial deposits / Limestone / Peat / Sandstones/ shales, blown sand / Others
Blown sand
Gleyed
Brown earths
Calcareous
Podzolised
Organic
Other
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 CategorySoil Type / Alluvium / Glacial till / Fluvial-Glacial deposits / Limestone / Peat / Sandstones/ shales, blown sand / Others
Blown sand
Gleyed
Brown earths
Calcareous
Podzolised
Organic
Other
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 CategorySoil Type / Alluvium / Glacial till / Fluvial-Glacial deposits / Limestone / Peat / Sandstones/ shales, blown sand / Others
Blown sand
Gleyed
Brown earths
Calcareous
Podzolised
Organic
Other
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) Using your knowledge of the properties of the soils and of the parent materials, suggest some ways in which parent materials are here influencing soil properties
g) Discuss ways in which the results of this study might be improved and the conclusions could be made more decisive.