Sample size and design effect SMU（SMU样本大小和设计效果）.pdfVIP

Sample size and design effect This presentation is a brief introduction to the design effect, which is an adjustment that should be used to determine survey sample size. Cluster sampling is commonly used, rather than simple random sampling, mainly as a means of saving money when, for example, the population is spread out, and the researcher cannot sample from everywhere. However, “respondents in the same cluster are likely to be somewhat similar to one another” 1 . As a result, in a clustered sample “Selecting an additional member from the same cluster adds less new information than would a completely independent selection”2 . Thus, for example, in single stage cluster samples, the sample is not as varied as it would be in a random sample, so that the effective sample size is reduced3. The loss of effectiveness by the use of cluster sampling, instead of simple random sampling, is the design effect. The design effect is basically the ratio of the actual variance, under the sampling method actually used, to the variance computed under the assumption of simple random sampling4,5,6 . For an example, “The interpretation of a value of (the design effect) of, say, 3.0, is that the sample variance is 3 times bigger than it would be if the survey were based on the same sample size but selected randomly. An alternative interpretation is that only one-third as many sample cases would be needed to measure the given statistic if a simple random sample were used instead of the cluster 7 sample with its (design effect) of 3.0” . The main components of the design effect are the intraclass correlation, and the cluster sample sizes. * 8,9 Thus, the design effect is calculated as follows : DEFF = 1 + δ (n – 1), where DEFF is the design effect, δ is the intraclass correlation for the statistic in question, and ,