Often in statistics research, a population is too large to collect data on. A sampling distribution of a statistic is created by taking repeated samples of a certain size. But the most accurate information will be gained by taking every possible sample of a certain size.

A population of size 4 has 6 possible samples of size 2. Use this fact to explain why taking every sample of a certain size is not done for a population too large to analyze.

Samples are used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient and manageable. When are populations used in research? Populations are used when a research question requires data from every member of the population.

Sample size determination is the process of determining the appropriate number of subjects to include in a study. The appropriate sample size is defined as the minimum sample size required to achieve an acceptable chance of achieving a statistical criterion of interest (e.g. statistical significance, maximum interval width) for a proposed study. The methodology used to determine the appropriate sample size varies depending on the type of testing procedure used, the underlying assumptions etc. In addition, most sample size calculations will require pre-study estimates for the outcome of interest and additional nuisance parameters.

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