How large should the sample be

When researchers ask the question, "How large should the sample be?" what they usually mean is "How small a sample can I get away with?" Therefore, the often quoted 'the larger, the better' principle is singularly unhelpful for them. Unfortunately, there are no hard and fast rules in setting the optimal sample size; the final answer to the 'how large/small?' question should be the outcome of the researcher considering several broad guidelines:

(1) In the survey research literature a range of between 1%-10% of the population is usually mentioned as the 'magic sampling fraction,' depending on how careful the selection has been (i.e., the more scientific the sampling procedures applied, the smaller the sample size can be, which is why opinion polls can produce accurate predictions from samples as small as 0.1% of the population).

(2) From a purely statistical point of view, a basic requirement is that the sample should have a normal distribution, and a rule of thumb to achieve this, offered by Hatch and Lazaraton (1991), is that the sample should include 30 or more people. However, Hatch and Lazaraton also emphasize that this is not an absolute rule, because smaller sample sizes can be compensated for by using certain special statistical procedures.

(3) From the perspective of statistical significance (cf. Section 4.3.6), the principal concern is to sample enough learners for the expected results to be able to reach statistical significance. Because in L2 studies meaningful correlations reported in journal articles have often been as low as 0.30 and 0.40, a good rule of thumb is that we need around 50 participants to make sure that these coefficients are significant and we do not lose potentially important results. However, certain multivariate statistical procedures require more than 50 participants; for factor analysis, for example, we need a minimum of 100 but preferably more subjects.

(4) A further important consideration is whether there are any distinct subgroups within the sample which may be expected to behave differently from the others. If we can identify such subgroups in advance (e.g., in most L2 studies of school children, girls have been found to perform differently from boys), we should set the sample size so that the minimum size applies to the smallest subgroup to allow for effective statistical procedures.

(5) When setting the final sample size, it is advisable to leave a decent margin to provide for unforeseen or unplanned circumstances. For example, some participants are likely to drop out of at least some phases of the project; some questionnaires will always have to be disqualified for one reason or another; and - in relation to Point 4 above - we may also detect unexpected subgroups that need to be treated separately.

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