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In statistical hypothesis testing, there are various notions of so-called type III errors (or errors of the third kind), and sometimes type IV errors or higher, by analogy with the type I and type II errors of Jerzy Neyman and Egon Pearson. Fundamentally, type III errors occur when researchers provide the right answer to the wrong question, i.e ...
In statistical hypothesis testing, a type I error, or a false positive, is the rejection of the null hypothesis when it is actually true. A type II error, or a false negative, is the failure to reject a null hypothesis that is actually false. [1] Type I error: an innocent person may be convicted. Type II error: a guilty person may be not convicted.
The notable unsolved problems in statistics are generally of a different flavor; according to John Tukey, [1] "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems." A list of "one or two open problems" (in fact 22 of them) was given by David Cox. [2]
In statistical hypothesis testing, this fraction is given the Greek letter α, and 1 − α is defined as the specificity of the test. Increasing the specificity of the test lowers the probability of type I errors, but may raise the probability of type II errors (false negatives that reject the alternative hypothesis when it is true). [a]
The statistical errors, on the other hand, are independent, and their sum within the random sample is almost surely not zero. One can standardize statistical errors (especially of a normal distribution) in a z-score (or "standard score"), and standardize residuals in a t-statistic, or more generally studentized residuals.
In statistics, the term "error" arises in two ways. Firstly, ... Secondly, it arises in the context of statistical modelling (for example regression) ...
Oldberg, T. (2005) "An Ethical Problem in the Statistics of Defect Detection Test Reliability," Speech to the Golden Gate Chapter of the American Society for Nondestructive Testing. Published on the Web by ndt.net; Stone, M. (2009) Failing to Figure: Whitehall's Costly Neglect of Statistical Reasoning, Civitas, London. ISBN 1-906837-07-4
For example, a researcher may wish to study the opinions of registered voters (target population) by calling residences listed in a telephone directory (sampling frame). Undercoverage may occur if not all voters are listed in the phone directory.