Sample Size Estimation



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Background
Questions about sample size are ubiquitous in research. Too small a sample will yield scant information; but ethics, economics, time and other constraints require that a sample size not be too large.
“How many subjects do I need?” Neither 7 nor 30 nor any number is an all-purpose answer. A sample size of 30 is a “large sample” in some textbook discussions of “normal approximation”; yet 30,000 observations still may be too few to assess a rare, but serious teratogenic effect. The best first response to “how many?” may be not a number, but a sequence of further questions. A study’s size and structure should depend on the research context, including the researcher’s objectives and proposed analyses.
If a survey is to be carried out for descriptive purposes such as assessing the prevalence of some characteristic, the sample size is based on the required precision of the prevalence estimate. For example, why are so many national opinion polls based on samples of approximately 1000 responses? And if the poll results are “valid” on a national level, how “valid” are they on a provincial level?
If there is a comparative aspect to the study, the sample size is based on how detailed a comparison is desired. Detecting very small differences requires larger samples than detecting large differences. The appropriate sample size also depends on the precision or variability of the data. Fewer replications are needed if a response variable changes little from one measurement to the next, than if the response varies wildly.
Sample sizes should also be computed with attention to dropout rates. If 100 subjects are enrolled at the beginning of a study, how many can be expected to remain at the end of the study, if a two-year or five-year follow-up is required? This “attrition rate” must be considered.
As well, more sophisticated analytic techniques may require larger samples than simple techniques.
A historical note: A landmark survey paper in the New England Journal of Medicine in 1978, by Freiman et al., brought to people’s attention the problem that “negative” findings from clinical trials may be a result of small sample sizes. Since that time, grant proposals and journal articles have included a discussion of the sample size issue.
In this module we will learn the questions to ask, and what to do with the corresponding answers, to provide the answer to THE QUESTION, “How many subjects do I need?”
One cautionary note: “How many subjects do I need?” is linked to the companion question, “How many subjects can I afford to get?” The final decision on sample size must pay attention to the various constraints on recruitment. Just as no responsible consumer should go shopping without first setting the limits on how much is available to spend, no decision on sample size should be made without assessing the corresponding affordability.

The First Set of Questions Before “THE QUESTION”




“THE QUESTION”  “How many subjects do I need?”

Two preliminary questions must be asked:

Question 1. Is the study descriptive or is the study comparative?

Question 2. Is the primary outcome variable a measurement variable (a.k.a. interval or

continuous) or is the primary outcome variable a categoric variable?

These are discussed below.





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