Sample size

How large should a sample be? There are several ways to answer this question? One answer depends on the purpose of the investigation. If the purpose is to explore some topic, sample size is not critical. Cases are selected until the investigator learns enough about the topic to meet his or her needs. For descriptive or explanatory studies, sample size is important because the size of a sample affects our ability to generalize results of the research.

Several factors have to be considered in deciding on the size of a sample. One is the heterogeneity of the population - how much the population varies with respect to any of the key variables being measured. A larger sample is needed for a population with a great deal of variation in contrast to a population in which persons are more alike. When there is relatively little variation in a population, say, by ethnic background or socio-economic status, a smaller sample can be used. When large differences exist within a population, a larger sample is needed to adequately reflect the variations in the population.

Another factor is the degree of accuracy desired for estimating the parameters in the population. Generally,   larger samples will provide more accurate estimates than a smaller one. In Chapter 19, you will see why this is true.

Sample size should also take into account the number of variables to be analyzed simultaneously. If variables are going to be analyzed one at a time, like describing means for ages of respondents, their years of schooling, or for measures of some attitude, smaller samples will do. When two or three variables are analyzed together, larger samples are necessary to ensure there are enough cases in the cells of the tables that will be involved. (See Chapter 17 and Chapter 18 foror more on this point).

There are precise ways to estimate how a sample should be to achieve a certain degree of accuracy for estimating population parameters, but these methods require detailed information about the population from which a sample is to be selected.   The necessary data often are not available. To overcome this problem, some commonly accepted guidelines can help in deciding about the size of a sample. The size of the population, which we generally know with reasonable accuracy, influences how these guidelines are applied. Strangely, the required sample size is inverse to the size of the population. For populations under 1,000, a sampling ratio of about 30% of the cases is recommended.   For a population of 10,000 or so, a 10% ratio is sufficient. As the population further increases, to 15,000 or larger, 1% of the cases can produce very accurate results. Random samples of 2,000 to 2,500 are usually accurate for populations in the millions.

The numbers mentioned may not be practical for individuals doing their own interviewing. Then, compromises have to be made. Statistical analyses, which we discuss in Part 4 of this book, should be based on a minimum of 30 cases, but at least 100 cases is recommended. The final size of a sample often is based on a compromise between larger ideal size and the largest practical size a researcher can manage. Researchers take into account the purpose of their study, the heterogeneity of the population being investigated, how precise they want the results to be (this requires some statistical knowledge which we present in Part 4 of this book), and make a decision.