Statistic

In statistics, there is an important distinction between a statistic and a parameter.

A statistical parameter or population parameter is a quantity entering into the probability distribution of a statistic or a random variable.

A statistic (singular) or sample statistic is any quantity computed from values in a sample, often the mean.

Samples are collected and statistics are calculated from the samples, so that one can make inferences or extrapolations from the sample to the population.

When a statistic is used to estimate a population parameter, is called an estimator.

An "estimator" or "point estimate" is a statistic (that is, a function of the data) that is used to infer the value of an unknown parameter in a statistical model.

When a statistic (a function) is being used for a specific purpose, it may be referred to by a name indicating its purpose: in descriptive statistics, a descriptive statistic is used to describe the data; in estimation theory, an estimator is used to estimate a parameter of the distribution (population); in statistical hypothesis testing, a test statistic is used to test a hypothesis.

A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.

The sample mean or empirical mean and the sample covariance are statistics computed from a collection (the sample) of data on one or more random variables.

In cases where that cannot be done, the standard deviation σ is estimated by examining a random sample taken from the population and computing a statistic of the sample, which is used as an estimate of the population standard deviation.

Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience.

In statistics, completeness is a property of a statistic in relation to a model for a set of observed data.

Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience.

In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter".

Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience.

Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal.

First Definition: The variance of a well-behaved statistical estimator is finite and one condition on its mean is that it is differentiable in the parameter being estimated.

Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures.

The most common is the Fisher information, which is defined on the statistic model induced by the statistic.

More generally, if is a statistic, then

A statistic (singular) or sample statistic is any quantity computed from values in a sample, often the mean.

Technically speaking, a statistic can be calculated by applying any mathematical function to the values found in a sample of data.

"Parameter" refers to any characteristic of a population under study.

Formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the unknown estimands; that is, the function is strictly a function of the data.

When a statistic (a function) is being used for a specific purpose, it may be referred to by a name indicating its purpose: in descriptive statistics, a descriptive statistic is used to describe the data; in estimation theory, an estimator is used to estimate a parameter of the distribution (population); in statistical hypothesis testing, a test statistic is used to test a hypothesis.

When a statistic (a function) is being used for a specific purpose, it may be referred to by a name indicating its purpose: in descriptive statistics, a descriptive statistic is used to describe the data; in estimation theory, an estimator is used to estimate a parameter of the distribution (population); in statistical hypothesis testing, a test statistic is used to test a hypothesis.

When a statistic (a function) is being used for a specific purpose, it may be referred to by a name indicating its purpose: in descriptive statistics, a descriptive statistic is used to describe the data; in estimation theory, an estimator is used to estimate a parameter of the distribution (population); in statistical hypothesis testing, a test statistic is used to test a hypothesis.