Geoscience Reference
In-Depth Information
1
11
21
31
41
51
61
71
81
91
101
111
2
12
22
32
42
52
62
72
82
92
102
3
13
23
33
43
53
63
73
83
93
103
113 114
4
14
24
34
44
54
64
74
84
94
104
5
15
25
35
45
55
65
75
85
95
105
115
6
16
26
36
46
56
66
76
86
96
106
7
17
27
37
47
57
67
77
87
97
107
117 118
8
18
28
38
48
58
68
78
88
98
108
9
19
29
39
49
59
69
79
89
99
109
10
20
30
40
50
60
70
80
90
100
110
112
116
119
120
FIGURE 2.1
A rectangular study area divided into 120 quadrats to be used as sample units. The numbers
shown in the quadrats are labels used for random sampling rather than the values of some
variable of interest.
the present case involves labeling the quadrats in the population from
1 to 120 (as in Figure 2.1) and then selecting the ones to sample by gen-
erating 12 random integers from 1 to 120 on a computer. If
R
is a com-
puter-generated random number in the range 0 to 1, then
Z
=
MIN
[120,
INT
(
R
× 120 + 1.0)] is a random integer in the range 1 to 120, where the
function
INT
(
x
) gives the integer part of
x
, and
MIN
(
a
,
b
) gives the mini-
mum of
a
and
b
. The minimum function is included here in case a value
of
R
= 1 can occur, in which case
INT
(
R
× 120 + 1.0) = 121.
Because sampling should be without replacement, the same quadrat
would not be allowed to occur more than once. Any repeated selections
would therefore be ignored and the process of selecting random integers
continued until 12 different quadrats have been chosen.
A table of random numbers such as Table 2.1 can also be used for the
selection of sample units. To use this table, first start at an arbitrary place
in the table such as the beginning of row 8. The first three digits in each
block of four digits can then be considered, to give the series 569, 362, 898,
287, 607, 099, 681, 779, 458, 883, 181, 001, 927, 280, 224, 831, 711, 207, 151, 180,
978, 773, 075, 367, 251, 106, 547, 711, 347, 720, 737, and so on. The first 12
different numbers between 1 and 120 then give a simple random sample
of quadrats, that is, 99, 1, 75, and so on.
Once the sample quadrats are chosen, these would be examined to
find the number of plants that each contains. The average for the 12 sam-
ple quadrats then gives an estimate of the mean number of plants in the
area of 1 quadrat over the entire study region, for which the likely level
of error can be determined by methods discussed next. If necessary, the
estimate and its error can then be converted so it is in terms of plants per
square meter or any other measure of density that is of interest.
