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Statistical inference
 
 
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Inferential statistics or statistical induction comprises the use of statistics
Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
 to make inference
Inference

Inference is the act or process of deriving a logical consequence from premises.Inference is studied within several different fields.* Human inference is traditionally studied within the field of cognitive psychology....
s concerning some unknown aspect of a population
Population

File:Population density.pngIn biology, a population is the collection of inter-breeding organisms of a particular species; in sociology, a collection of human beings....
. It is distinguished from descriptive statistics
Descriptive statistics

Descriptive Statistics are used to describe the basic features of the data gathered from an experimental study in various ways. A descriptive Statistics is distinguished from inductive statistics....
.

Two schools of inferential statistics are frequency probability
Frequency probability

Frequency probability is the Probability interpretations that defines an event's probability as the limit of its relative frequency in a large number of trials....
 and Bayesian inference
Bayesian inference

Bayesian inference is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true....
.

Definition
Statistical inference is inference about a population from a random sample drawn from it or, more generally, about a random process from its observed behavior during a finite period of time.






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Encyclopedia


Inferential statistics or statistical induction comprises the use of statistics
Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
 to make inference
Inference

Inference is the act or process of deriving a logical consequence from premises.Inference is studied within several different fields.* Human inference is traditionally studied within the field of cognitive psychology....
s concerning some unknown aspect of a population
Population

File:Population density.pngIn biology, a population is the collection of inter-breeding organisms of a particular species; in sociology, a collection of human beings....
. It is distinguished from descriptive statistics
Descriptive statistics

Descriptive Statistics are used to describe the basic features of the data gathered from an experimental study in various ways. A descriptive Statistics is distinguished from inductive statistics....
.

Two schools of inferential statistics are frequency probability
Frequency probability

Frequency probability is the Probability interpretations that defines an event's probability as the limit of its relative frequency in a large number of trials....
 and Bayesian inference
Bayesian inference

Bayesian inference is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true....
.

Definition


Statistical inference is inference about a population from a random sample drawn from it or, more generally, about a random process from its observed behavior during a finite period of time. It includes:

  1. point estimation
    Point estimation

    In statistics, point estimation involves the use of statistical sample data to calculate a single value which is to serve as a "best guess" for an unknown population parameter....
  2. interval estimation
    Interval estimation

    In statistics, interval estimation is the use of Sampling data to calculate an interval of possible values of an unknown population parameter, in contrast to point estimation, which is a single number....
  3. hypothesis testing (or statistical significance
    Statistical significance

    In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. "A statistically significant difference" simply means there is statistical evidence that there is a difference; it does not mean the difference is necessarily large, important, or significant in the common meaning of the word....
     testing)
  4. prediction
    Prediction

    A prediction is a statement or claim that a particular event will occur in the future in more certain terms than a forecasting. The etymology of this word is Latin ....


There are several distinct schools of thought about the justification of statistical inference. All are based on some idea of what real world phenomena can be reasonably modeled as probability
Probability

Probability, or wikt:chance, is a way of expressing knowledge or belief that an Event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about t...
.
  1. frequency probability
    Frequency probability

    Frequency probability is the Probability interpretations that defines an event's probability as the limit of its relative frequency in a large number of trials....
  2. Bayesian probability
    Bayesian probability

    Bayesian probability interprets the concept of probability as 'a measure of a state of knowledge' , and not as a frequentist . Broadly speaking, there are two views on Bayesian probability that interpret the 'state of knowledge' concept in different ways....
  3. fiducial probability


The topics below are usually included in the area of statistical inference.
  1. Statistical assumptions
    Statistical assumptions

    Statistical assumptions are general assumptions about statistical populations.Statistics, like all mathematical disciplines, does not generate valid conclusions from nothing....
  2. Likelihood principle
    Likelihood principle

    In statistics,the likelihood principle is a controversial principle of statistical inference which asserts that all of the information in a Sampling is contained in the likelihood function....
  3. Estimating parameters
    Estimation theory

    Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data....
  4. Statistical hypothesis testing
    Statistical hypothesis testing

    A statistical hypothesis test is a method of making statistical decisions using experimental data. It is sometimes called confirmatory data analysis, in contrast to exploratory data analysis....
  5. Revising opinions in statistics
    Revising opinions in statistics

    Researchers who use personal probability can proceed as follows:*A statistical model for the data generating process is assumed. The model might specify that the data follows a normal distribution with an unknown mean....
  6. planning statistical research
  7. summarizing statistical data


See also

  • Descriptive statistics
    Descriptive statistics

    Descriptive Statistics are used to describe the basic features of the data gathered from an experimental study in various ways. A descriptive Statistics is distinguished from inductive statistics....
  • Induction (philosophy)


Further reading

  • Lenhard, Johannes (2006). "Models and Statistical Inference: The Controversy between Fisher and Neyman—Pearson," British Journal for the Philosophy of Science, Vol. 57 Issue 1, pp. 69-91.
  • Sudderth, William D. (1994). "Coherent Inference and Prediction in Statistics," in Prawitz, Skyrms, and Westerstahl (eds.), Logic, Methodology and Philosophy of Science IX: Proceedings of the Ninth International Congress of Logic, Methodology and Philosophy of Science, Uppsala, Sweden, August 7-14, 1991, Amsterdam: Elsevier.
  • Trusted, Jennifer (1979). The Logic of Scientific Inference: An Introduction, London: The Macmillan Press, Ltd.


External links

  • MIT : Statistical Inference