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.
