Sample Statistic Value

A Sample Statistic Value is a numeric value produced by a random sample-based statistical measure when applied to a statistical sample.

AKA: Sample Statistic, Statistic Value, Observed Statistic, Calculated Statistic, Empirical Statistic Value, Sample Estimate Value.
Context:
- It can typically represent a Point Estimate of a population parameter computed from sample data.
- It can typically be defined mathematically as t=g(s) where s=(x₁,x₂,...,xₙ) is a statistical sample and g is a random sample-based statistical measure.
- It can typically serve as input to Statistical Decision Procedures and hypothesis tests.
- It can typically be accompanied by Standard Error estimates quantifying its sampling variability.
- It can typically be used to construct Confidence Intervals around population parameter estimates.
- It can often be aggregated into Statistic Datasets for meta-analysis and comparative studies.
- It can often exhibit Sampling Distribution properties when collected across multiple random samples.
- It can often be transformed into Standardized Statistic Values for cross-sample comparison.
- It can often be reported with Significance Levels and p-values in statistical reports.
- It can often vary from the True Parameter Value by an amount called Sampling Error.
- It can range from being a Point Sample Statistic Value to being an Interval Sample Statistic Value, depending on its precision specification.
- It can range from being a Univariate Sample Statistic Value to being a Multivariate Sample Statistic Value, depending on its dimensionality.
- It can range from being a Descriptive Sample Statistic Value to being an Inferential Sample Statistic Value, depending on its analytical purpose.
- It can range from being a Biased Sample Statistic Value to being an Unbiased Sample Statistic Value, depending on its expectation property.
- It can range from being a Precise Sample Statistic Value to being an Imprecise Sample Statistic Value, depending on its variance magnitude.
- It can have associated Uncertainty Measures such as standard errors or confidence intervals.
- It can be computed using Statistical Software Systems that apply random sample-based statistical measures.
- It can be stored in Statistical Databases for longitudinal analysis and trend monitoring.
- It can be visualized using Statistical Plots and data visualization techniques.
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Example(s):
- Central Tendency Sample Statistic Values, such as:
  - 37.1 as the Sample Mean Value of age in city C.
  - 42 as the Sample Median Value of income in region R.
  - "Category A" as the Sample Mode Value of preference in survey S.
  - 35.8 as the Trimmed Sample Mean Value excluding outliers.
- Dispersion Sample Statistic Values, such as:
  - 15.3 as the Sample Standard Deviation Value of test scores.
  - 234.09 as the Sample Variance Value of measurements.
  - 48 as the Sample Range Value between minimum and maximum.
  - 12.5 as the Sample Interquartile Range Value of distribution.
- Association Sample Statistic Values, such as:
  - 0.85 as the Sample Correlation Coefficient Value between variables.
  - -23.4 as the Sample Covariance Value of paired observations.
  - 0.72 as the Cohen's Kappa Value for inter-rater agreement.
- Test Sample Statistic Values, such as:
  - 2.45 as the t-Statistic Value for mean comparison.
  - 7.82 as the Chi-Square Statistic Value for independence test.
  - 3.21 as the F-Statistic Value for variance comparison.
  - 1.96 as the Z-Statistic Value for standardized test.
  - 0.03 as the P-Value for significance testing.
- Performance Sample Statistic Values, such as:
  - 0.92 as the Accuracy Value of a classification model.
  - 0.88 as the Precision Value for positive predictions.
  - 0.95 as the Recall Value for sensitivity measurement.
  - 0.91 as the F1 Score Value combining precision and recall.
  - 0.87 as the AUC-ROC Value for classifier performance.
- Count-Based Sample Statistic Values, such as:
  - 145 as the Count Value of occurrences.
  - 0.23 as the Proportion Value of success rate.
  - 0.15 as the Prevalence Value in population screening.
- Economic Sample Statistic Values, such as:
  - 0.41 as the Gini Coefficient Value measuring inequality.
  - 1.23 as the Elasticity Value of demand.
  - 108.3 as the Price Index Value for inflation tracking.
- Time Series Sample Statistic Values, such as:
  - 0.76 as the Autocorrelation Value at lag 1.
  - -0.34 as the Partial Autocorrelation Value at lag 2.
  - 0.82 as the Cross-Correlation Value between series.
- Video Game Statistic Values, such as:
  - 95.2 as the Win Rate Value in competitive gaming.
  - 2.8 as the Kill-Death Ratio Value in shooter games.
  - 345 as the Score Value in arcade games.
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Counter-Example(s):
- Population Parameter, which represents true values rather than sample-based estimates.
- Population Parameter Values, such as:
  - Population Mean Value (μ) requiring complete population data.
  - Population Variance Value (σ²) based on all population values.
  - Population Proportion Value (p) from census data.
- Theoretical Value, which is derived from mathematical models rather than empirical data.
- Probability Value (in the theoretical sense), which represents likelihoods rather than observed statistics.
- Random Variable, which represents potential outcomes rather than realized values.
- Statistical Measure, which is the function rather than its output value.
- Raw Data Value, which is an individual observation rather than a summary value.
- Predicted Value, which is a model output rather than a sample summary.
See: Random Sample-based Statistical Measure (the function that produces it), Statistical Sample, Statistical Population, Population Parameter, Test Statistic, Point Estimate, Sampling Distribution, Sampling Error, Standard Error, Confidence Interval, Statistical Inference, Descriptive Statistic, Statistic Dataset, Statistical Hypothesis Testing.

References

2016

(Stat Trek, 2016) ⇒ "Populations and Samples", © 2011, Encyclopedia of Mathematics] Retrieved October 11, 2016, from http://stattrek.com/sampling/populations-and-samples.aspx
- QUOTE: Other differences have to do with nomenclature, notation, and computations. For example, a measurable characteristic of a population, such as a mean or standard deviation, is called a parameter; but a measurable characteristic of a sample is called a statistic.

(Wikipedia, 2016) ⇒ https://www.wikiwand.com/en/Statistic
- A statistic (singular) or sample statistic 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.

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.

2011

http://en.wikipedia.org/wiki/Statistic
- … The term statistic is used both for the function and for the value of the function on a given sample.

2009

(WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=statistic
- S: (n) statistic (a datum that can be represented numerically)