Chapter 10: Processes of Perception and Analysis

Section 9: Statistical Analysis

Practical statistics

The vast majority of statistical analysis is in practice done on continuous numerical data. And with surprising regularity it is assumed that random variations in such data follow a Gaussian distribution (see page 976). But while this may sometimes be true—perhaps as a consequence of the Central Limit Theorem—it is rarely checked, making it likely that many detailed inferences are wrong. So-called robust statistics uses for example medians rather than means as an attempt to downplay outlying data that does not follow a Gaussian distribution.

Classical statistical analysis mostly involves trying to use data to estimate parameters in specific probabilistic models. Non-parametric statistics and related methods often claim to derive conclusions without assuming particular models for data. But insofar as a conclusion relies on extrapolation beyond actual measured data it must inevitably in some way use a model for data that has not been measured.

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From Stephen Wolfram: A New Kind of Science [citation]