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In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously [1] or estimates a subset of parameters selected based on the observed values. [2] The larger the number of inferences made, the more likely erroneous inferences become.
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.
The process by which a conclusion is inferred from multiple observations is called inductive reasoning. The conclusion may be correct or incorrect, or correct to within a certain degree of accuracy, or correct in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to ...
Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.
Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. [29] Inferential statistical analysis infers properties of a population , for example by testing hypotheses and deriving estimates.
Design-based assumptions. These relate to the way observations have been gathered, and often involve an assumption of randomization during sampling. [6] [7] The model-based approach is the most commonly used in statistical inference; the design-based approach is used mainly with survey sampling. With the model-based approach, all the ...
Hochberg & Tamhane (1987) defined "family" as "any collection of inferences for which it is meaningful to take into account some combined measure of error". [3] According to Cox (1982), a set of inferences should be regarded a family: [citation needed] To take into account the selection effect due to data dredging