Module H6 Session 03: Selecting Random Numbers
Session 03 – Simple and Stratified Random Sampling
How to do random sampling
Tables of random numbers should have totally unconnected digits, i.e. where any of the
integers 0, 1, 2 ... 8, 9 is equally likely in any space regardless of what numbers appear
elsewhere. Purely for convenience of reading, the numbers are printed in blocks of pairs of
digits.
For each separate random sample from a population of size N, start at a newly chosen
random point. Use as many columns as there are digits in the largest number N you might
sample. If the population contains N = 12 individuals indexed by numbers 1, 2, 3, ... 10,
11, 12, you have to think of these as 01, 02, 03, ... 09, 10, 11, 12. Then you need 2 columns
because these are 2-digit numbers.
Go down the chosen pair of columns, if necessary continuing to the next pair on the page.
Write down the numbers between 1 and N as they occur. Ignore 00, N + 1, N + 2, etc. up
to 99. Ignore repetitions of the same digit pair.
Example
To take a sample of size 4 from a population of size 12, start (for example) at row three of
columns 9 and 10, to get:
90
75
70
01
03
52
72
60
as the first few numbers. Ignore 90, 75, 70 as being bigger than 12, but select 01, 03, 09,
06. So the selected random sample of size 4 contains the individuals indexed by numbers
1, 3, 6, and 9 in the population.
SADC Course in Statistics
Module H6 Session 03 Selecting Random Numbers – Page 1
Module H6 Session 03: Selecting Random Numbers
Suppose the process is repeated to take a second random sample of size four, from the
same population of size 12, starting at the top of columns 13 and 14. The resulting sample
would contain individuals indexed by numbers 04, 07, 11, 06, i.e. individuals 4, 6, 7, and 11
of the list.
A more complicated way of sampling using random number tables is to read each digit pair
as the remainder after dividing the number by N. With N = 12, we would then use 01, 13,
25, 37, ... 85 as representing 1, ... 11, 23, 35, ... for 11, and 12, 24, 96 as representing 12. We
would ignore 00, and 97, 98, 99. This takes more time, so don't do it. It is sometimes
suggested so as to use the random numbers more economically, but this should not really
be necessary. Programs like Excel or SPSS, will generate random numbers if required.
Example
44
85
44
47
03
59
90
33
57
20
62
22
29
22
54
26
58
88
52
20
82
52
90
75
70
51
90
49
74
56
04
22
07
53
77
19
76
55
11
59
45
95
69
76
95
98
70
50
11
60
40
91
27
12
54
91
14
71
96
30
24
61
29
17
61
41
71
93
70
13
01
03
52
72
60
45
40
89
76
50
51
15
64
17
61
98
69
78
93
56
22
44
32
38
40
54
46
97
26
20
83
27
40
51
95
32
17
89
66
22
99
25
21
17
63
29
61
88
48
34
30
91
56
26
58
06
76
84
96
91
19
19
11
00
78
71
54
75
83
22
11
99
74
81
50
32
73
88
23
22
93
42
42
66
73
83
02
42
71
05
73
33
13
67
53
70
18
33
54
85
80
33
66
79
63
88
55
00
25
18
71
96
18
64
06
85
66
37
34
47
64
88
58
82
71
44
38
80
15
00
02
22
94
10
73
80
89
45
30
39
12
81
64
05
21
24
32
84
07
94
34
32
17
21
01
78
72
28
34
84
22
48
06
59
28
50
92
57
18
20
57
95
71
85
50
02
75
96
95
35
SADC Course in Statistics
Module H6 Session 03 Selecting Random Numbers – Page 2