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Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling.Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model.
Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures. The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method.
Statistical procedures for finding differences between groups, along with interactions between the groups that were included in an experiment or study, can be classified along two dimensions: 1) were the statistical contrasts that will be evaluated decided upon prior to collecting the data (planned) or while trying to figure out what those data ...
Statistical hypothesis testing is a key technique of both frequentist inference and Bayesian inference, although the two types of inference have notable differences. Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect. The procedure ...
Bootstrapping is a procedure for estimating the distribution of an estimator by resampling (often with replacement) one's data or a model estimated from the data. [1] Bootstrapping assigns measures of accuracy ( bias , variance, confidence intervals , prediction error, etc.) to sample estimates.
Random experiments are often conducted repeatedly, so that the collective results may be subjected to statistical analysis. A fixed number of repetitions of the same experiment can be thought of as a composed experiment, in which case the individual repetitions are called trials. For example, if one were to toss the same coin one hundred times ...
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.
Mathematical statistics is a key subset of the discipline of statistics. Statistical theorists study and improve statistical procedures with mathematics, and statistical research often raises mathematical questions.