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Extrapolating from 'sample' to 'population'

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The basic idea of statistics is simple:

You want to use limited amounts of data to make general conclusions.

To do this, statisticians have developed methods based on a simple model: Assume that an infinitely large population of values exists and that your data (your 'sample') was randomly selected from this population. Analyze your sample and use the rules of probability to make inferences about the overall population.

This model is an accurate description of some situations. For example, quality control samples really are randomly selected from a large population. Clinical trials do not enroll a randomly selected sample of patients, but it is usually reasonable to extrapolate from the sample you studied to the larger population of similar patients.

In a typical experiment, you don't really sample from a population, but you do want to extrapolate from your data to a more general conclusion. The concepts of sample and population can still be used if you define the sample to be the data you collected and the population to be the data you would have collected if you had repeated the experiment an infinite number of times.

The problem is that the statistical inferences can only apply to the population from which your samples were obtained, but you often want to make conclusions that extrapolate even beyond that large population. For example, you perform an experiment in the lab three times. All the experiments used the same cell preparation, the same buffers, and the same equipment. Statistical inferences let you make conclusions about what would probably happen if you repeated the experiment many more times with that same cell preparation, those same buffers, and the same equipment.

You probably want to extrapolate further to what would happen if someone else repeated the experiment with a different source of cells, freshly made buffer, and different instruments. Unfortunately, statistical calculations can't help with this further extrapolation. You must use scientific judgment and common sense to make inferences that go beyond the limitations of statistics.



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