Sampling 4 : How big should a sample be?

 

Delia Chiaro

 

Among the most frequently asked questions raised by students starting out on research within the ESP we will surely find “How many people do I need to interview?” or “How many questionnaires do I need to administer?” which can be summed up in “How big should my sample be?” And these questions certainly mirror the equally frequent set of queries which can be summed up in “But you only have only interviewed 200 people, what about the other 58, 999 million Italians/Brits/Spaniards etc.”. Well, first of all, let us not forget that a survey is not a census. In other words surveys do not set out to assess the whole population but just a representative sample of that population. I am using the term “population” in a very particular way. In empirical research the term population refers to a group of interest. In other words, a population can indeed be made up of  people living in the same country or who belong to the same ethnic group, but it can also consist of people of the same profession, of the same generation, with the same interests or with just about any common denominator we can think of which will be relevant to what we are researching.

 

Having said that, how can we be sure that say, the opinions of 1,500 respondents normally interviewed in surveys by professional polling associations in the USA are representative of 250 million people? The answer is that respondents are carefully selected to reflect a representative sample. Now, according to probability theory, error is always present in a sample but the bigger the sample, the less chance there is for error to occur. However, such common sense is only true up to a point. Let us imagine we have a packet of our favourite biscuits. We can be pretty sure that all the biscuits will be more or less the same shape, colour, size, taste and consistency. In other words, if two or three biscuits are alike, the others in the pack are likely to be the same too. Furthermore, if we were to buy another four packs of the same biscuits, they are also likely to be the same. Of course, one or two may be broken and perhaps even over-baked, but most of those biscuits will be pretty similar even if we were to buy all the stock on sale in three different supermarkets. Therefore, according to statisticians, pretty accurate information can be obtained (within 3% or even less either way) from 1,500 people and that a sample even 10 times larger would not be any more accurate.

 

Having said that, another question raised by skeptics is the following “If 75% of my sample hold a particular view, what does this mean? Can I say 75% of the whole group in which I am interested (for example, 75% of all German interpreters believes x) or can I only say 75% of those interpreters who answered my questionnaire believe x?” If we have collected our data correctly, the choice of the right statistical test will lead us to infer information gathered from our sample to the entire population.  Exit polls during elections are a good example of how, by interviewing a certain quota of voters, chosen randomly across a nation, usually leads to pretty accurate forecasts over and above those few respondents who typically are jokers and/or liars.

 

Determining the size of a sample can either be done through statistical techniques (the Google search engine provides thousands of hits for software to determine sample size) or through what are known as ad hoc methods. The problem with statistical techniques is that they do not take into account costs involved in obtaining information, thus, in the field, an entirely different approach tends to be adopted. What is known as an ad hoc method can be carried out when a person knows from experience how to establish feasible sample size notwithstanding budget constraints. Sudman suggest that a sample should be large enough to be divided into groups of 100 or more, with sub-groups of respondents of between 20 and 50, the assumption being that less accuracy is needed in a sub-group. But what about students working not only with budget constraints, but also with strict deadlines? Can they realistically work in terms of triple figures? Surely not.

 

Given that students are normally involved in exploratory research, the commonsensical answer is to guide them to work with manageable, convenient and realistic samples. For a tentative investigation, according to mathematicians, 30 seems to be a magic number. In the type of cross-cultural/language investigations typical in translation and interpreting, this would lead to, say, two parallel samples of 30+30 (or multiples of 30); in other words, small, manageable, but with which significant results could be drawn with the use of the right statistical test – and specific tests for small samples do exist. As long as we are aware of the fact that our study is a small one and that it is exploratory in nature and not the final word on the matter, such hypothetical studies would be perfectly respectable examples of quantitative research.

 

References:

David A. Aaker; V. Kumar and George S. Day. Marketing Reseach 5th Edition. 1995. New York: John Wiley. 392-395.

Seymour Sudman. Applied Sampling. New York: Academic Press, 1976, 50.