Populations, samples, and sampling distributions
To this point, we have used regression analysis only to describe the relationship between two variables in a sample. However, in statistical analysis, we are not usually interested in the characteristics of a particular sample. More often, we are interested in estimating the characteristics of the population from which the sample was drawn. Whenever we wish to make statements about the characteristics of a population, based on the characteristics of a sample, we must rely on the logic of statistical inference. In particular, we must employ the concept of sampling distributions. Indeed, the logic of inferential statistics is based largely on the concept of sampling distributions. A sampling distribution is the theoretical distribution of a sample statistic that would be obtained from a large number of random samples of equal size from a population. Consequently, the sampling distribution serves as a statistical “bridge” between a known sample and the unknown population. Sample statistics, such as the sample mean and variance, are used to provide estimates of corresponding population parameters, such as the population mean and variance.
KeywordsSample Statistic Statistical Inference Central Limit Theorem Sampling Distribution Population Parameter
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