Statistic
A statistic (singular) or sample statistic is any quantity computed from values in a
When a statistic is used for estimating a population parameter, the statistic is called an
A
Examples
Some examples of statistics are:
- "In a recent survey of Americans, 52% of Republicans say global warming is happening."
In this case, "52%" is a statistic, namely the percentage of Republicans in the survey sample who believe in global warming. The population is the set of all Republicans in the United States, and the population parameter being estimated is the percentage of all Republicans in the United States, not just those surveyed, who believe in global warming.
- "The manager of a large hotel located near Disney World indicated that 20 selected guests had a mean length of stay equal to 5.6 days."
In this example, "5.6 days" is a statistic, namely the mean length of stay for our sample of 20 hotel guests. The population is the set of all guests of this hotel, and the population parameter being estimated is the mean length of stay for all guests.[2] Whether the estimator is unbiased in this case depends upon the sample selection process; see the inspection paradox.
There are a variety of functions that are used to calculate statistics. Some include:
- sample median, and sample mode
- Sample variance and sample standard deviation
- Sample quantiles besides the median, e.g., quartiles and percentiles
- chi-squared statistic, f statistic
- Order statistics, including sample maximum and minimum
- Sample moments and functions thereof, including kurtosis and skewness
- Various functionals of the empirical distribution function
Properties
Observability
Statisticians often contemplate a
Statistical properties
Important potential properties of statistics include
, and computational convenience.Information of a statistic
Information of a statistic on model parameters can be defined in several ways. The most common is the
See also
- Statistics
- Statistical theory
- Descriptive statistics
- Statistical hypothesis testing
- Summary statistic
- Well-behaved statistic
References
- ^ Kokoska 2015, p. 296-308.
- ^ Kokoska 2015, p. 296-297.
- Kokoska, Stephen (2015). Introductory Statistics: A Problem-Solving Approach (2nd ed.). New York: W. H. Freeman and Company. ISBN 978-1-4641-1169-3.
- Parker, Sybil P (editor in chief). "Statistic". McGraw-Hill Dictionary of Scientific and Technical Terms. Fifth Edition. McGraw-Hill, Inc. 1994. ISBN 0-07-042333-4. Page 1912.
- DeGroot and Schervish. "Definition of a Statistic". Probability and Statistics. International Edition. Third Edition. Addison Wesley. 2002. ISBN 0-321-20473-5. Pages 370 to 371.