### Chapter 5. Sampling: Sampling Distributions

### Sampling Distributions

In inferential statistics, sample statistics are used as an estimate of their corresponding population parameter. Since a sample does not include all individuals from a population, it is highly unlikely that a sample will be a perfect representation of the population it is drawn from. As a result, some *sampling error* is to be expected.

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Sampling error

The difference between a sample statistic and its corresponding population parameter is called the **sampling error**.

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There are a large number of different samples of a particular size that can be drawn from any given population. Each of these samples will be made up out of different individuals and as a result, sample statistics are going to vary from sample to sample. Some of these sample statistics will overestimate the true population parameter, whereas other sample statistics will underestimate it. A sample statistic can thus be considered a *random variable*.

Fortunately, the degree to which a sample statistic is expected to differ from the true population parameter can be predicted fairly accurately using a number of mathematical theorems. Specifically, these theorems are used to determine what the *sampling distributions *of the sample statistics look like.

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Sampling Distribution

The **sampling distribution **of a sample statistic is the *probability distribution* of that statistic.

In other words, it is the distribution of the sample statistic if you were to endlessly draw samples of a particular size from the population.

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