- Sampling is the process of taking a smaller group of subjects/scores from a larger population. In statistical inference, we test hypotheses about the population using samples.
- Samples do not replicate the population. The discrepancy between sample values and population scores is known as sampling error.
- The sampling distribution is what we use to help us decide whether a particular sample came from a given (or known) population. It tells us what to expect when we draw one sample from a larger population.
- A sampling distribution is the frequency distribution of the value of a statistic calculated on an infinite number of samples of a given size drawn from a known population.
- To test hypotheses, we place the value of a statistic for a single sample on the sampling distribution. If the sampling distribution shows a low probability (unexpected), then we conclude that the sample did not come from the population. If the sampling distribution shows a high proability (expected), then we conclude that the sample did come from the population.
- Every statistic has a sampling distribution.
- Sampling distributions vary in shape depending on what statistic is used and either the sample size or degrees of freedom for that statistic.
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