In a very general sense, the larger the sample, the better -- because larger samples tend to be more similar to the population from which they are drawn. However, if the population of interest is small, then the sample can be relatively small. Large samples require more time for data collection and analysis, and are therefore more costly than smaller ones.
If a treatment is known to have a fairly strong effect, it may show up in an experiment involving a small sample. On the other hand, a small sample for a survey may miss individuals holding a minority point of view. For surveys one has to consider refusal and spoilage rates (incomplete responses, illegible answers, nonsensical replies). In such cases the researcher should aim for a larger sample in order to cover the losses.
Increasing the number of variables and/or their levels requires more participants. For example, comparing attitudes of 20 lower division and 20 upper division college students toward college athletics may be a reasonable number. If the samples of 20 each are broken down into fraternity/sorority vs. non-greek students, the number in each category declines. A gender division leads to only 5 persons per cell -- probably too small for drawing any conclusions.
Level Greek Gender
Appropriate sample size depends on
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