In general, each statistic is an estimate of a parameter, whose value is not known exactly. Every number found using a sample is just an (approximation|estimation) of a parameter (the truth).
- 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.
A statistic is a descriptive number::
- any number that describes the individuals
- a measure or number that summarizes the individuals in a sample.
- a numerical measure that describes a characteristic of a sample
- Sample size: The number of Student (unit)
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.
- a quantity calculated from a sample.
- Average Age of Students
Sampling error implies that they will vary from one study to the next (from one data set to another).
A statistic describes a sample whereas a population parameter describes the population. A statistic is an observable random variable, which differentiates it both from a population parameter that is a generally unobservable quantity.
A statistic may not be representative for every individuals in the sample
The number of captured individuals is a statistic as it deals with the sample. The actual population is a parameter that we are trying to estimate.
A statistic is called parametric when we are trying to make inferences about population parameters, based on a sample.