Statistics calculated on a sample do not fully match the corresponding statistics for the population being studied, but they are generally different. When we perform an experiment, we examine a sample of individuals, but our primary interest is to draw general conclusions about the entire population from which our sample was obtained. In other words, the main research question is “what can we possibly say about the population, after having seen the sample?” The process by which we look at the results of an experiment to draw more general conclusions is named statistical inference, and it is traditionally based on the so-called frequentist confidence interval, which is an interval of values that can “capture” the real underlying population value for the statistic under study, with high confidence and small probability of error. In this chapter, simple methods for obtaining confidence intervals are provided, and the limitations of the frequentist confidence intervals are discussed.

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A Brief Intro to Statistical Inference

  • Andrea Onofri

摘要

Statistics calculated on a sample do not fully match the corresponding statistics for the population being studied, but they are generally different. When we perform an experiment, we examine a sample of individuals, but our primary interest is to draw general conclusions about the entire population from which our sample was obtained. In other words, the main research question is “what can we possibly say about the population, after having seen the sample?” The process by which we look at the results of an experiment to draw more general conclusions is named statistical inference, and it is traditionally based on the so-called frequentist confidence interval, which is an interval of values that can “capture” the real underlying population value for the statistic under study, with high confidence and small probability of error. In this chapter, simple methods for obtaining confidence intervals are provided, and the limitations of the frequentist confidence intervals are discussed.