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..."The noncentral chi-squared distribution with zero degrees of freedom and testing for uniformity", ''[[Biometrika]]'', 66, 381–386</ref> [[Category:Statistical hypothesis testing]] ...

In [[statistical hypothesis testing]], the error exponent of a hypothesis testing procedure is the rate at which the probabilities of Type I and Type II deca ...\infty}\frac{-\ln P_\text{error}}{n}</math>. Error exponents for different hypothesis tests are computed using [[Sanov's theorem]] and other results from [[large ...

...probability of [[Type I error#Type I error|falsely rejecting]] the [[null hypothesis]]. That is, it is the probability of making a [[type I error]]. It is denot For a [[simple hypothesis]], ...

...ability&nbsp;1. Dembo and Peres (1994) proved the existence of almost sure hypothesis tests. ...1.2}</math> would be one example). But even using that bandwidth, if the testing was done in batches of 10, then ...

{{Short description|Non-parametric statistical test}} ...of similarities (ANOSIM)''' is a [[Nonparametric statistics|non-parametric statistical test]] widely used in the field of [[ecology]]. The test was first suggeste ...

{{short description|Statistical hypothesis testing measure}} ...ue, the ''q''-value gives the expected pFDR obtained by rejecting the null hypothesis for any result with an equal or smaller ''q''-value.<ref>{{Cite journal|las ...

...or of a book on [[statistical hypothesis test]]s, ''Statistical Hypothesis Testing in Context: Reproducibility, Inference, and Science'' (with Michael P. Fay, Brittain's book on hypothesis testing was a finalist in mathematics and statistics in the 2023 [[PROSE Awards]].{ ...

{{Short description|Statistical test}} ...egrated of order]] 1. It builds on the [[Dickey–Fuller test]] of the null hypothesis <math>\rho = 1</math> in <math>\Delta y_{t}= (\rho -1)y_{t-1}+u_{t}\,</math ...

{{Short description|Chance of wrongly rejecting the null hypothesis}} ...bability]] of falsely rejecting the [[null hypothesis]] for a particular [[hypothesis test|test]]. The false positive rate is calculated as the ratio between the ...

...]] experiments and other modern applications, there are a huge number of [[Statistical parameter|parameters]], often tens of thousands or more and it is very impo ...59.pdf Theoretical Results Needed for Applying the False Discovery Rate in Statistical Problems]. April, 2001 (Section 3.2, Page 51)</ref> ...

{{for|use in statistical testing|Statistical model}} .... An appropriate null model behaves in accordance with a reasonable [[null hypothesis]] for the behavior of the system under investigation. ...

...dent trials. Annals of Mathematical Statistics (27):713–721.</ref> In some statistical applications, the standard binomial variance estimator can be used even if ...s and the [[statistical hypothesis testing#the testing process|alternative hypothesis]] is true for other tests, then success probabilities are likely to differ ...

...Central Limit Theorem]], allowing the use of Z-statistics for [[hypothesis testing]] and [[confidence interval]] estimation. It is used in various fields to c ==== Hypothesis test ==== ...

...c methods may lead to misleading conclusions or may fail to detect truly [[Statistical significance|significant]] results from [[experiment]]s. ...nal statistical methods do not provide exact solutions to such problems as testing [[variance components]] or [[ANOVA]] under unequal variances, exact tests f ...

...imit Theorem]], allowing the construction of a [[z-test]] for [[hypothesis testing]] and [[confidence interval]] estimation. It is used in various fields to c == Hypothesis test == ...

...of equality of variances''' is a [[statistical test|test]] for the [[null hypothesis]] that two [[normal distribution|normal]] populations have the same [[varia ...ample variance]]s.<ref>Snedecor, George W. and Cochran, William G. (1989), Statistical Methods, Eighth Edition, Iowa State University Press.</ref> This particular ...

{{Short description|Statistical test}} ...ed by measure space are equivalent for all groups. A rejection of the null hypothesis means that either the centroid and/or the spread of the objects is differen ...

...t statistic would have approximately a chi-square distribution if the null hypothesis is true. In minimum chi-square estimation, one finds the values of paramet ...following data set. It is desired to [[hypothesis test|test]] the [[null hypothesis]] that the population from which this sample was taken follows a [[Poisson ...

...njunction with [[statistical hypothesis testing|hypothesis testing]]. A "[[statistical significance|statistically significant]]" difference between two proportion ...umb]] criteria set out by Cohen.<ref name="Cohen 1988">{{cite book | title=Statistical Power Analysis for the Behavioral Sciences | author=Cohen, Jacob | year=198 ...

...in the context of examining certain point patterns, whereas in most other statistical contexts it is referred to the concept of a spatial Poisson process.<ref na ...to distinguish these from arbitrary points of the region in question. The hypothesis of complete spatial randomness for a spatial point pattern asserts that the ...