Sampling Fundamentals - Determining the Sample Size: Ad Hoc Methods
Sampling Fundamentals - Determining the Sample Size: Ad Hoc Methods
How large should the sample be? This question is simple and straightforward, but to answer it with precision is not so easy. Statistical theory does provide some tools and a structure with which to address the question which will be described in more detail in Chapter 12. In this chapter several ad hoc but practical approaches are discussed.
Rules of Thumb
One approach is to use some rulesof thumb. Sudman suggests that the sample should be large enough so that when it is divided into groups, each group will have a minimum sample size of 100 or more.6
Suppose the opinions of citizens regarding municipal parks was desired. In particular, an estimation was to be made of the percentage who fell that tennis courts were needed. Suppose, further, that a comparison was desired among those who (1) used parks frequently, (2) used parks occasionally, and (3) never used parks. Thus, the sample size should be such that each of these groups had at least 100 people. If the frequent park users, the smallest group, were thought to be about 10 percent of the population.
then under simple random sampling a sample size of 1000 would be needed to generate a group of 100 subjects.
In almost every study, a comparison between groups provides useful information and is often the motivating reason for the study. It is therefore necessary to consider the smallest group and to make sure that it is of sufficient size to provide the needed reliability.
In addition to considering comparisons between major groups, the analysis might consider subgroups. For example, there could be an interest in breaking down the group of frequent park users by age and comparing the usage by teenagers, young adults, middle-aged persons, and senior citizens. Sudman suggests that for such minor breakdowns the minimum sample size in each subgroup should be 20 to 50.7 The assumption is that the accuracy needed for the subgroups is less. Suppose that the smallest subgroup of the frequent park users, the senior citizens, is about one percent of the population and it is desired to have 20 in each subgroup. Under simple random sampling, a sample size of about 2000 might be recommended in this case.
If one of the groups or subgroups of the population is a relatively small percentage of the population, then it is sensible to use disproportionate sampling. Suppose only 10 percent of the population watches educational television, and opinions of this group are to be compared with others in the population. If telephone interviewing were involved, people might be contacted randomly until 100 people were identified who do not watch educational television. The interviewing then would continue, but all respondents would be screened, and only those who watch educational television would be interviewed. The result would be a sample of 200, half of which watch educational television.
Budget Constraints
Often a strict budget constraint exists. A museum director can spare $500 for a study and no more. If data analysis will require $ 100 and a respondent interview is $5, then the maximum affordable sample size is 80. The question then becomes whether a sample size of 80 is worthwhile or if the study should be changed or simply not conducted.
Comparable Studies
Another approach is to find similar studies and use their sample sizes as a guide. The studies should be comparable in terms of the number of groups
into which the sample is divided for comparison purposes. They also should have achieved a satisfactory level of reliability.
Table 11-5, which is based on a summary of several hundred studies, provides a very rough idea of typical sample size. Note that the typical sample size tends to be larger for national studies than for regional studies. A possible reason is that the national studies generally address issues with more financial impact and therefore require a bit more accuracy. Note, also, that samples involving institutions tend to be smaller than those involving people or households. The reason is probably that institutions are more costly to sample than people.
Factors Determining Sample Size
Sample size really depends on fayrfactors. The first is the number of groups and subgroups within the sample that will be analyzed. The second is the value of the information in the study in general and the accuracy required of the results in particular. At one extreme, the research need not be conducted if the study is of little importance. The third is the cost of the sample A cost-benefit analysis must be considered.TfFsampllng costs are low, a larger sample size can be justified than if sampling costs are high. Thejnjal. factor is the variability of the population. If all members of the population have identical opinions on an Issue, a sample of one is satisfactory. As the variability within the population increases, the sample size also will need to be larger. Chapter 12 will provide the interested reader with another perspective on sample size determination.
How large should the sample be? This question is simple and straightforward, but to answer it with precision is not so easy. Statistical theory does provide some tools and a structure with which to address the question which will be described in more detail in Chapter 12. In this chapter several ad hoc but practical approaches are discussed.
Rules of Thumb
One approach is to use some rulesof thumb. Sudman suggests that the sample should be large enough so that when it is divided into groups, each group will have a minimum sample size of 100 or more.6
Suppose the opinions of citizens regarding municipal parks was desired. In particular, an estimation was to be made of the percentage who fell that tennis courts were needed. Suppose, further, that a comparison was desired among those who (1) used parks frequently, (2) used parks occasionally, and (3) never used parks. Thus, the sample size should be such that each of these groups had at least 100 people. If the frequent park users, the smallest group, were thought to be about 10 percent of the population.
then under simple random sampling a sample size of 1000 would be needed to generate a group of 100 subjects.
In almost every study, a comparison between groups provides useful information and is often the motivating reason for the study. It is therefore necessary to consider the smallest group and to make sure that it is of sufficient size to provide the needed reliability.
In addition to considering comparisons between major groups, the analysis might consider subgroups. For example, there could be an interest in breaking down the group of frequent park users by age and comparing the usage by teenagers, young adults, middle-aged persons, and senior citizens. Sudman suggests that for such minor breakdowns the minimum sample size in each subgroup should be 20 to 50.7 The assumption is that the accuracy needed for the subgroups is less. Suppose that the smallest subgroup of the frequent park users, the senior citizens, is about one percent of the population and it is desired to have 20 in each subgroup. Under simple random sampling, a sample size of about 2000 might be recommended in this case.
If one of the groups or subgroups of the population is a relatively small percentage of the population, then it is sensible to use disproportionate sampling. Suppose only 10 percent of the population watches educational television, and opinions of this group are to be compared with others in the population. If telephone interviewing were involved, people might be contacted randomly until 100 people were identified who do not watch educational television. The interviewing then would continue, but all respondents would be screened, and only those who watch educational television would be interviewed. The result would be a sample of 200, half of which watch educational television.
Budget Constraints
Often a strict budget constraint exists. A museum director can spare $500 for a study and no more. If data analysis will require $ 100 and a respondent interview is $5, then the maximum affordable sample size is 80. The question then becomes whether a sample size of 80 is worthwhile or if the study should be changed or simply not conducted.
Comparable Studies
Another approach is to find similar studies and use their sample sizes as a guide. The studies should be comparable in terms of the number of groups
into which the sample is divided for comparison purposes. They also should have achieved a satisfactory level of reliability.
Table 11-5, which is based on a summary of several hundred studies, provides a very rough idea of typical sample size. Note that the typical sample size tends to be larger for national studies than for regional studies. A possible reason is that the national studies generally address issues with more financial impact and therefore require a bit more accuracy. Note, also, that samples involving institutions tend to be smaller than those involving people or households. The reason is probably that institutions are more costly to sample than people.
Factors Determining Sample Size
Sample size really depends on fayrfactors. The first is the number of groups and subgroups within the sample that will be analyzed. The second is the value of the information in the study in general and the accuracy required of the results in particular. At one extreme, the research need not be conducted if the study is of little importance. The third is the cost of the sample A cost-benefit analysis must be considered.TfFsampllng costs are low, a larger sample size can be justified than if sampling costs are high. Thejnjal. factor is the variability of the population. If all members of the population have identical opinions on an Issue, a sample of one is satisfactory. As the variability within the population increases, the sample size also will need to be larger. Chapter 12 will provide the interested reader with another perspective on sample size determination.
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