Abstract
The starting point of a statistical analysis is a set of data, for example, of counts or measurements. One aim may be simply to study what these data have to tell us. If they consist of a set of real numbers we might want to see, for example, whether they are small or large; tightly concentrated or spread out, whether they are stable or tend to increase with time, etc. If they are points in the plane we can get an idea of the shape of this set of points, for example, whether they cluster about a line. The branch of statistics dealing with this kind of investigation used to be called descriptive statistics, but now goes by the name data analysis or, more precisely, exploratory data analysis (EDA), a term introduced by Tukey (see Exploratory Data Analysis: Univariate Methods. Instead we consider how we can quantify the conclusions or decisions drawn from an analysis. Frequentist inference requires that any quantifying measure be interpretable in terms of frequentist probability of events (see Frequentist Interpretation of Probability). That is, we assume the data are random quantities produced by some probability distribution and that something is known about this distribution. For example, if we have a set of n measurements of some quantity, we may assume that these measurements are independently and identically distributed. We may stop there or may go further and make some assumptions about this common distribution.
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Rojo, J. (2012). Frequentist Inference. In: Rojo, J. (eds) Selected Works of E. L. Lehmann. Selected Works in Probability and Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1412-4_91
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