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Psychological statistics is application of formulas, theorems, numbers and laws to psychology. Statistical methods for psychology include development and application statistical theory and methods for modeling psychological data. These methods include psychometrics, factor analysis, experimental designs, and Bayesian statistics. The article ...
In statistics, a nuisance parameter is any parameter which is unspecified [1] but which must be accounted for in the hypothesis testing of the parameters which are of interest. The classic example of a nuisance parameter comes from the normal distribution , a member of the location–scale family .
A "parameter" is to a population as a "statistic" is to a sample; that is to say, a parameter describes the true value calculated from the full population (such as the population mean), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the sample mean). Thus a "statistical parameter" can be more ...
In the theory of stochastic processes in probability theory and statistics, a nuisance variable is a random variable that is fundamental to the probabilistic model, but that is of no particular interest in itself or is no longer of any interest: one such usage arises for the Chapman–Kolmogorov equation.
When the theoretical distribution of a statistic of interest is complicated or unknown. Since the bootstrapping procedure is distribution-independent it provides an indirect method to assess the properties of the distribution underlying the sample and the parameters of interest that are derived from this distribution.
Conceptually, a confidence distribution is no different from a point estimator or an interval estimator (confidence interval), but it uses a sample-dependent distribution function on the parameter space (instead of a point or an interval) to estimate the parameter of interest. A simple example of a confidence distribution, that has been broadly ...
The parameter , in turn, is partitioned into (,), where is the parameter of interest, and is the nuisance parameter. For concreteness, ψ {\displaystyle \psi } might be the population mean, μ {\displaystyle \mu } , and the nuisance parameter λ {\displaystyle \lambda } the standard deviation of the population mean, σ {\displaystyle \sigma } .
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.