# Random Sample-based Statistic Function

A Random Sample-based Statistic Function is a statistic function that receives a random population sample.

## References

### 2016

1. Upton, G., Cook, I. (2006). Oxford Dictionary of Statistics, OUP. ISBN 978-0-19-954145-4

### 2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/statistic Retrieved:2015-2-23.
• A statistic (singular) is a single measure of some attribute of a sample (e.g., its arithmetic mean value). It is calculated by applying a function (statistical algorithm) to the values of the items of the sample, which are known together as a set of data.

More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution; that is, the function can be stated before realization of the data. The term statistic is used both for the function and for the value of the function on a given sample.

A statistic is distinct from a statistical parameter, which is not computable because often the population is much too large to examine and measure all its items. However, a statistic, when used to estimate a population parameter, is called an estimator. For instance, the sample mean is a statistic that estimates the population mean, which is a parameter.

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. However, a single statistic can be used for multiple purposes – for example the sample mean can be used to describe a data set, to estimate the population mean, or to test a hypothesis.

### 2013

• (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/Statistic
• A statistic (singular) is a single measure of some attribute of a sample (e.g., its arithmetic mean value). It is calculated by applying a function (statistical algorithm) to the values of the items of the sample, which are known together as a set of data.

More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution; that is, the function can be stated before realization of the data. The term statistic is used both for the function and for the value of the function on a given sample.

A statistic is distinct from a statistical parameter, which is not computable because often the population is much too large to examine and measure all its items. However, a statistic, when used to estimate a population parameter, is called an estimator. For instance, the sample mean is a statistic that estimates the population mean, which is a parameter.

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. However, a single statistic can be used for multiple purposes – for example the sample mean can be used to describe a data set, to estimate the population mean, or to test a hypothesis.

### 2009

• http://planetmath.org/encyclopedia/SampleVariance.html
• QUOTE: A statistic, or sample statistic, [math]S[/math] is simply a function, usually real-valued, of a set of (sample) data or observations [math]X=(X_1,X_2,...,X_n)[/math]. [math]S = S(X)[/math]. More formally, let O be the sample space of the data X, then [math]S[/math] is a function from O to some set [math]T[/math], usually a subset of R^k. The data X is usually considered as a vector of iid random variables X_i.

### 2006

• (Dubnicka, 2006k) ⇒ Suzanne R. Dubnicka. (2006). “Introduction to Statistics - Handout 11." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
• TERMINOLOGY : Once a random sample has been selected, one typically measures or records the value of one or more variables of interest for each subject in the sample. Collectively, these observations/measurements are the data. Once the data have been collected, one typically summarizes the data in one or more different ways. In general, the types of summaries used are (1) graphical displays and (2) statistics. A statistic is simply a numerical summary measure of a sample. Therefore, a statistic is a property of some sort of the sample. Ideally, if our sample is representative of the population, we will use this statistic as our best guess that the corresponding parameter value. A parameter is a numerical summary meausure of a population; that is, a parameter is a property of a population.
• TERMINOLOGY : Recall that a statistic is a summary measure of the sample which is a set of random variables. Thus, a statistic is also a random variable. This is why is makes sense to compute the expectation and variance of a statistic. Also, as a statistic is a random variable also has a distribution associated with it. The distribution of a statistic is called the sampling distribution of the statistic.