A simple random sample gives each member of the population an equal chance of being chosen. It is not a haphazard sample as some people think! One way of achieving a simple random sample is to number each element in the sampling frame (e.g. give everyone on the Electoral register a number) and then use random numbers to select the required sample.
Random numbers can be obtained using your calculator, a spreadsheet, printed tables of random numbers, or by the more traditional methods of drawing slips of paper from a hat, tossing coins or rolling dice.
The optimum sample is the one which maximises precision per unit cost, and by this criterion simple random sampling can often be bettered by other methods.
Advantages
Ideal for statistical purposes
Disadvantages
- Hard to achieve in practice
- Requires an accurate list of the whole population
- Expensive to conduct as those sampled may be scattered over a wide area
1.3.1 RANDOM NUMBERS FROM A CALCULATOR OR SPREADSHEET
Most electronic calculators have a RAN# function that produces a random decimal number between 0 and 1. The formula =RAND ( ) in Excel achieves the same result, but to more decimal places. So how can you use these to select a random sample?
Suppose you wanted to select a random lottery number between 1 and 49. There are two approaches.
Firstly, you could multiply the electronic random number by 49 to get a random number between 0 and 49; Round this number up to the nearest whole number. For example, if the electronic random number is 0.497, when multiplied by 49 this gives 24.353, which you should round up to 25.
Secondly, you could treat the electronic random number as a series of random digits and use the first two as your random number, ignoring any that are greater than 49. For example, the electronic random number 0.632 has first two digits 63 and you ignore it, whereas 0.317 gives the random number 31.
1.3.2 RANDOM NUMBER TABLES
Random number tables consist of a randomly generated series of digits (0-9). To make them easy to read there is typically a space between every 4th digit and between every 10th row. When reading from random number tables you can begin anywhere (choose a number at random) but having once started you should continue to read across the line or down a column and NOT jump about.
Here is an extract from a table of random sampling numbers:
3680 2231 8846 5418 0498 5245 7071 2597
If we were doing market research and wanted to sample two houses from a street containing houses numbered 1 to 48 we would read off the digits in pairs
36 80 22 31 88 46 54 18 04 98 52 45 70 71 25 97
and take the first two pairs that were less than 48, which gives house numbers 36 and 22.
If we wanted to sample two houses from a much longer road with 140 houses in it we would need to read the digits off in groups of three:
368 022 318 846 541 804 985 245 707 1 25 97
and the numbers underlined would be the ones to visit: 22 and 125.
Houses in a road usually have numbers attached, which is convenient (except where there is no number 13). In many cases, however, one has first to give each member of the population a number. For a group of 10 people we could number them as:
| 0 |
Appleyard |
5 |
Francis |
| 1 |
Banyard |
6 |
Gray |
| 2 |
Croft |
7 |
Hibbert |
| 3 |
Durran |
8 |
Jones |
| 4 |
Entwhistle |
9 |
Lillywhite |
By numbering them from 0 to 9 you need only use single digits from the random number table. 36802231884654180498524570712597. In this case the first digit is 3 and so Durran is chosen.