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Data Collection - Random Sampling

Simple random sampling

Simple random sampling can be carried out in two ways – the lottery method and using random numbers.

Lottery Method

The lottery method involves:

  • transferring each person’s name from the list and putting it on a piece of paper
  • the pieces of paper are placed in a container and thoroughly mixed
  • the required number are selected by someone without looking
  • the names selected are the simple random sample.

This is basically similar to a game of bingo or the national lottery. This procedure is easy to carry out especially if both population and sample are small, but can be tedious and time consuming for large populations or large samples.

Alternatively random numbers can be used. Random numbers are strings of digits that have been generated by the lottery method and can be found in books of statistical tables. An example of these is:

03

47

43

73

86

   

36

96

47

36

61

97

74

24

67

62

 

42

81

14

57

20

16

76

62

27

66

 

56

50

26

71

07

12

56

85

99

26

 

96

96

68

27

31

55

59

56

35

64

 

38

04

80

46

22

Random numbers tend to be written in pairs and blocks of 5 by 5 to make reading easy. However, care is needed when reading these tables. The numbers can be read in any direction but they should be read as a singe string of digits i.e. left to right as 0, 3, 4, 7 etc’, or top to bottom as 0, 9, 1, 1, 5, 3, 7, … etc. It is usual to read left to right.

Random Number Method

The random number method involves:

  • Allocating a number to each person on the list (each number must consist of the same number of digits so that the tables can be read consistently).
  • Find a starting point at random in the tables (close your eyes and point).
  • Read off the digits.
  • The names matching the numbers are the sample units.

For the example of selecting nine people at random from 90:

A

The sampling frame is the list of 90 people. Number this list 00, 01, 02, …, 89. Note that each number has two digits and the numbering starts from 00.

B

Suppose a starting point is found at random from the random number tables and let this number be 16. Then the person that has been numbered 16 is the first sample unit.

C

Let the next two digits be 76, then the person numbered 76 is the second sample unit.

This procedure is repeated until the nine people have been identified.

D

Any number occurring for second time is ignored as is any two-digit number over 89.

  1. A sampling frame is required. This may not be available, exist or be incomplete
  2. The procedure is unbiased but the sample may be biased. For instance, if the 90 people are a mixture of men and women and all men were selected this would be a biased sample.

To overcome this problem a stratified sample can be taken. In this the population structure is reflected in the sample structure, with respect to some criterion.

For example, suppose the 90 people consist of 30 men and 60 women. If gender is the criterion for stratification then:

30

of the sample should be men

90

ie.

30

x 9 = 3 men

90

60

of the sample should be women

90

ie.

60

x 9 = 6 women

90

Thus the sample reflects the population structure in terms of gender.

The three men and six women would then be selected by simple random sampling e.g., random numbers.

The problem with this approach is the criterion for stratification, (e.g., age, sex, job description), is chosen by you – it is subjective and may not be the best or more appropriate criterion. Also a more detailed sampling frame is required.

Back to the Sampling Page