Sampling and Sampling Methods

Simple Random Sampling

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
  

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.

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:
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.

Systematic Sampling

This is random sampling with a system! From the sampling frame, a starting point is chosen at random, and thereafter at regular intervals. For example, suppose you want to sample 8 houses from a street of 120 houses.

120/8=15, so every 15th house is chosen after a random starting point between 1 and 15. If the random starting point is 11, then the houses selected are 11, 26, 41, 56, 71, 86, 101,
and 116.

If there were 125 houses, 125/8=15.625, so should you take every 15th house or every 16th house? If you take every 16th house, 8*16=128 so there is a risk that the last house chosen does not exist. To overcome this the random starting point should be between 1 and
10. On the other hand if you take every 15th house, 8*15=120 so the last five houses will never be selected. The random starting point should now be between 1 and 20 to ensure that every house has some chance of being selected.

In a random sample every member of the population has an equal chance of being chosen, which is clearly not the case here, but in practice a systematic sample is almost always
acceptable as being random.

Advantages

• spreads the sample more evenly over the population
  
• easier to conduct than a simple random sample
  

Disadvantages

• the system may interact with some hidden pattern in the population, e.g. every third house along the street might always be the middle one of a terrace of three
  

Cluster Sampling

In cluster sampling the units sampled are chosen in clusters, close to each other.
Examples are households in the same street, or successive items off a production line.


The population is divided into clusters, and some of these are then chosen at random.
Within each cluster units are then chosen by simple random sampling or some other method. Ideally the clusters chosen should be dissimilar so that the sample is as representative of the population as possible.

Advantages

• saving of travelling time, and consequent reduction in cost
  
• useful for surveying employees in a particular industry, where individual companies can form the clusters
  

Disadvantages

• units close to each other may be very similar and so less likely to represent the whole population
  
• larger sampling error than simple random sampling
  

Quota Sampling

In quota sampling the selection of the sample is made by the interviewer, who has been given quotas to fill from specified sub-groups of the population. For example, an interviewer may be told to sample 50 females between the age of 45 and 60.

There are similarities with stratified sampling, but in quota sampling the selection of the sample is non-random. Anyone who has had the experience of trying to interview people in the street knows how tempting it is to ask those who look most helpful, hence it is not the most representative of samples, but extremely useful.

	Advantages quick and cheap to organise
	Disadvantages not as representative of the population as a whole as other sampling methods because the sample is non-random it is impossible to assess the possible sampling error

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