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Key Concepts

Parametric statistics

https://en.wikipedia.org/wiki/Parametric_statistics

Parametric statistics is a branch of statistics which assumes that sample data comes from a population that can be adequately modelled by a probability distribution that has a fixed set of parameters.^[1] Conversely a non-parametric model differs precisely in that the parameter set (or feature set in machine learning) is not fixed and can increase, or even decrease, if new relevant information is collected.^[2]

Most well-known statistical methods are parametric.^[3] Regarding nonparametric (and semiparametric) models, Sir David Cox has said, "These typically involve fewer assumptions of structure and distributional form but usually contain strong assumptions about independencies".^[4]

Non-parametric statistics

https://en.wikipedia.org/wiki/Category:Nonparametric_statistics

Nonparametric statistics is a branch of statistics concerned with non-parametric statistical models and non-parametric statistical tests. Non-parametric statistics are statistics that do not estimate population parameters. In contrast, see parametric statistics.

Nonparametric models differ from parametric models in that the model structure is not specified a priori but is instead determined from data. The term nonparametric is not meant to imply that such models completely lack parameters but that the number and nature of the parameters are flexible and not fixed in advance. Nonparametric models are therefore also called distribution free.

Nonparametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the frequency distributions of the variables being assessed.

Pearson's chi square test (goodness of fit)

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