Selection on grounds of convenience is not appropriate
Suppose that a number of people are assembled in a large theatre, say, the University auditorium, for a lecture and it is desired to draw a sample from the audience for the purpose of eliciting their views about the presentation. One way that might suggest itself to us would be to simply select any convenient group, say, people in the front row. Now, it is not hard to think of reasons why people in the front row might not be representative of the whole audience. Can you think of one or two? This method of selection is therefore not appropriate.
Haphazard selection is not appropriate also
An alternative method that might suggest itself to us would be to stand on the rostrum and pinpoint “haphazardly” persons to form part of the sample. It is perhaps not as easy to pick any fault with this approach but it is nevertheless faulted. Can you think why? Well the reason is that the individual doing the selection may, for example, have a preference, conscious or unconscious, for young persons so that once again the sample would not be representative of the whole population. It has been found, time and again, that when the task of picking a sample is left to a human being, biases tend to creep in, one way or another. Assuming that a particular researcher felt that he or she was free from biases or prejudices of any sort and could therefore safely proceed personally to the selection of a required sample, it would still be impossible for him or her to prove to the rest of the world that the sample were free from any bias whatsoever. Findings based thereon and extended to the whole population would be subject to challenge on grounds of subjectivity.
A Random Selection Procedure
Suppose that, instead of the above, all members of the audience are asked to write their names on bits of paper which are then scrapped and placed in a basket. The bits of paper are mixed thoroughly by shaking the basket and a sample is then drawn by picking out some bits of paper from the basket. Now this is a truly random procedure which is not subject to biases arising in the way described above. This method of carrying out random selection is not very practical especially if the size of the population is large. However, we shall see that there exists other more practical ones.
Why is random selection required?
In spite of it being random, the procedure just described could nevertheless occasionally yield samples similar to the ones obtainable under either the first or second procedures described above. So what has been gained? Well there are three very important advantages:
(i) With the first two procedures, any bias present would persist even if the selection process were repeated many times, always in the same direction. We refer to such biases as systematic biases. For example if an assistant was asked to select animals for an experiment and, for one reason or another, he tended to over represent larger animals in his selection, this bias would persist in repetitions of the selection with the same assistant. With the third procedure described, there is no systematic bias. In a single sample, larger animals may well be over represented but in repetitions of the selection, the biases will not always be in the same direction but rather tend to cancel out.
(ii) Even more interesting is the fact that, with the third procedure described, as the sample size increases, the risk of having an unrepresentative sample decreases. On the other hand, the potential biases in the first two procedures do not diminish with increases in the sample size. Think why?
characteristic. In other words it is possible to indicate the likely margins of error in the sample result.( This is done through the notion of confidence intervals, by application of sampling theory and is outside the scope of this course.) No such margins can be quoted when sampling is non-random.
Definition of random selection
Definition: Random (or probability) sampling is a method of sampling where every
member of the target population has a known, non-zero probability of selection.
Note that equal chance of selection is not a requirement of random selection. In fact, as we shall see later, there are instances where there are valid reasons for wanting certain sections of a population to be over-represented and others to be underrepresented. So long as every one has a chance of being selected and that chance is known, such over or under- representation is not a problem and can be compensated at the analysis stage by a technique known as re-weighting.
11.2.4 Representativeness
As we have seen, although randomisation eliminates systematic and persistent biases, it does not guarantee a representative sample, particularly when the sample is small. For example, consider a large population made up of men and women in equal proportions. If we draw a sample of ten persons from this population by simple random sampling, we may very well end up with eight men and two women. This is clearly a sample that is unrepresentative in terms of gender. If we had drawn a sample of 100, the risk of having a similarly unrepresentative sample, i.e. 80 men and 20 women would be considerably less. However, whatever the size of our sample, we could easily have forced it to be representative on the gender criterion by selecting half of our sample from men and the other half from women.
The objective of sampling is to try to capture into the sample the variation in the target population in respect of the characteristic or characteristics under study. To be certain to do this requires prior knowledge of the distributions such characteristics in the population which is , of course not available. What we can do however, is to ensure representativeness in
terms of other known characteristics of the population such as age, gender, occupation, etc which we suspect may be correlated to with the characteristic or characteristics under study. This is the idea underlying stratified sampling which is discussed in 11.2.9 below.
Randomisation alone does ensure a valid sample and produces valid estimates with margins of error that can be calculated by the application of statistical theory. Stratified sampling using relevant stratification factors gives additional guarantee of representativeness resulting in smaller margins of error.