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Sampling Distributions and Approximations

  • Douglas A. Wolfe
  • Grant Schneider
Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

Now that we have built a solid foundation based on exploratory data analysis techniques, proper design of experiments, and basic probability, we will put the finishing touches on this foundation by studying sampling distributions, the most important part of statistical inference. Before we can use the information we have collected and analyzed from our sample to make inferences about the population of interest, we must make sure that we understand how the statistic we have computed varies with repeated sampling. Our goal here is to describe what might happen if we repeat the entire sampling process and computation of the desired statistic again and again. Do you think that if you take a different sample you will get exactly the same value for the statistic? While it is certainly possible that this could happen, in most practical settings it is very unlikely that you will get exactly the same value of the statistic. At first, it might appear that this would be a major problem for the field of statistics. If we collect different samples and they usually give us different results, how can we make any inferences? The fact is that even though the values of the statistic are likely to differ from sample to sample, they will follow a pattern. This pattern of variation in repeated sampling is described by the sampling distribution of the statistic.

Supplementary material

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Douglas A. Wolfe
    • 1
  • Grant Schneider
    • 2
  1. 1.Department of StatisticsThe Ohio State UniversityColumbusUSA
  2. 2.Upstart NetworkSan CarlosUSA

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