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Probability distribution of the test statistic under the null hypothesis
the null distribution is the probability distribution of the test statistic when the null hypothesis is true. For example, in an F-test, the null distribution
Null_distribution
Statistical test comparing two probability distributions
samples. The null distribution of this statistic is calculated under the null hypothesis that the sample is drawn from the reference distribution (in the one-sample
Kolmogorov–Smirnov_test
Statistical hypothesis test
{\displaystyle p} -value by comparing T {\displaystyle T} to its distribution under the null hypothesis. The ranks are defined so that R i {\displaystyle
Wilcoxon_signed-rank_test
Position that there is no relationship between two phenomena
The null hypothesis (often denoted H 0 {\textstyle H_{0}} ) is the claim in scientific research that the effect being studied does not exist. The null hypothesis
Null_hypothesis
Continuous probability distribution
George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis
F-distribution
Similarity measure for number sequences
within them. Null distribution: For data which can be negative as well as positive, the null distribution for cosine similarity is the distribution of the dot
Cosine_similarity
Noncentral generalization of the chi-squared distribution
generalization of the chi-squared distribution. It often arises in the power analysis of statistical tests in which the null distribution is (perhaps asymptotically)
Noncentral chi-squared distribution
Noncentral_chi-squared_distribution
Probability distribution
that the given data set {x1, ..., xn} comes from a normal distribution. Typically the null hypothesis H0 is that the observations are distributed normally
Normal_distribution
Method of statistical inference
drawn from a given population." Thus the null hypothesis is that a population is described by some distribution predicted by theory. He uses as an example
Statistical_hypothesis_test
Statistical method
determine the p-value for X2. The distribution of X2 is a chi-squared distribution for the following reason; under the null hypothesis for test i, the p-value
Fisher's_method
Function of the observed sample results
test is called a null hypothesis test. As our statistical hypothesis will, by definition, state some property of the distribution, the null hypothesis is
P-value
Statistical test for normality of data
test the null hypothesis that data come from a normally distributed population, when the null hypothesis does not specify which normal distribution; i.e.
Lilliefors_test
Statistical hypothesis test
follows a χ2 frequency distribution. The purpose of the test is to evaluate how likely the observed frequencies would be assuming the null hypothesis is true
Chi-squared_test
Evaluates how likely it is that any difference between data sets arose by chance
approximation of the distribution of χ 2 {\displaystyle \chi ^{2}} . Sustain or reject the null hypothesis that the observed frequency distribution is the same
Pearson's_chi-squared_test
Probability distribution
distributed when the difference tested is null, the noncentral distribution describes how t is distributed when the null is false. This leads to its use in statistics
Noncentral_t-distribution
Nonparametric test of the null hypothesis
statistical test of the null hypothesis that randomly selected values X and Y from two populations have the same distribution. The value of U calculated
Mann–Whitney_U_test
observed data. In certain chi-square tests, one rejects a null hypothesis about a population distribution if a specified test statistic is too large, when that
Minimum_chi-square_estimation
Measure of spatial autocorrelation
under the null hypothesis of no spatial autocorrelation is E ( I ) = − 1 N − 1 {\displaystyle E(I)={\frac {-1}{N-1}}} The null distribution used for this
Moran's_I
Concept in inferential statistics
one end of the null distribution and is twice the size (5% vs. 2.5%) of each rejection region for a two-tailed test. As a result, the null hypothesis can
Statistical_significance
Type of probability distribution
F(p,n_{x}+n_{y}-1-p).} The non-null distribution of this statistic is the noncentral F-distribution (the ratio of a non-central Chi-squared random
Hotelling's T-squared distribution
Hotelling's_T-squared_distribution
Statistic used in statistical hypothesis testing
important property of a test statistic is that its sampling distribution under the null hypothesis must be calculable, either exactly or approximately
Test_statistic
Study of collection and analysis of data
an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical
Statistics
Statistical Markov model
significance. What is the probability that a sequence drawn from some null distribution will have an HMM probability (in the case of the forward algorithm)
Hidden_Markov_model
Statistical hypothesis testing measure
{\displaystyle D_{i}=0} ), then T i {\displaystyle T_{i}} follows the null distribution F 0 {\displaystyle F_{0}} ; while if H 1 {\displaystyle H_{1}} is
Q-value_(statistics)
Statistical test
the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. Z-test tests the mean of a distribution. For
Z-test
American singer-songwriter musician (born 1965)
two albums, Ghosts I–IV and The Slip, independently on his own label, The Null Corporation. In 2009, Nine Inch Nails went on hiatus following the Wave Goodbye
Trent_Reznor
Bioinformatics method
test in order to produce a null distribution for the ES. The P value is determined by comparison to the null distribution. Calculating significance this
Gene_set_enrichment_analysis
Probability distribution
the distribution of Spearman's rank correlation coefficient ρ, in the null case (zero correlation) is well approximated by the t distribution for sample
Student's_t-distribution
Non-parametric method for testing whether samples originate from the same distribution
of an identically shaped and scaled distribution for all groups, except for any difference in medians, then the null hypothesis is that the medians of all
Kruskal–Wallis_test
Probability distribution and special case of gamma distribution
the χ 2 {\displaystyle \chi ^{2}} -distribution with k {\displaystyle k} degrees of freedom is the distribution of a sum of the squares of k {\displaystyle
Chi-squared_distribution
Probability distribution
PMC 2821031, PMID 20157626. Johnstone, I. M. (2009), "Approximate null distribution of the largest root in multivariate analysis", Annals of Applied Statistics
Tracy–Widom_distribution
Statistical measure
this measure for use as a test statistic, and calculation of the null distribution of this test statistic. Mathematics portal Correlation Kendall's tau
Hoeffding's_independence_test
Online forum board
Nulled was an online cracking forum. In 2016, Nulled suffered a data breach, which helped law enforcement to obtain information about possible 'suspects'
Nulled
Statistical hypothesis test
Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value
Student's_t-test
Statistical hypothesis test
the random variable F, and checks if it follows an F-distribution. This check is valid if the null hypothesis is true and standard assumptions about the
F-test
Generalization of the one-dimensional normal distribution to higher dimensions
similarity to the multivariate normal distribution. The null hypothesis is that the data set is similar to the normal distribution, therefore a sufficiently small
Multivariate normal distribution
Multivariate_normal_distribution
Continuous probability distribution
probability theory and statistics, the Weibull distribution /ˈwaɪbʊl/ is a continuous probability distribution. It models a broad range of random variables
Weibull_distribution
Probability distribution on complex matrices
statistics, the complex Wishart distribution is a complex version of the Wishart distribution. It is the distribution of n {\displaystyle n} times the
Complex_Wishart_distribution
Term in statistical hypothesis testing
statistics, power is the probability of detecting an effect (i.e. rejecting the null hypothesis) given that some prespecified effect actually exists using a given
Power_(statistics)
Type of probability distribution
multivariate distributions with the chiral index, which takes values in the interval [0;1], and which is null if and only if the distribution is mirror symmetric
Symmetric probability distribution
Symmetric_probability_distribution
Observed inability to reproduce scientific studies
specification of prior distributions in the absence of hard data. A simplified version of the Bayesian argument, based on testing a point null hypothesis was
Replication_crisis
Statistical theorem
approaches the chi-squared ( χ 2 {\displaystyle \chi ^{2}} ) distribution under the null hypothesis H 0 {\displaystyle H_{0}} . Here, Λ {\displaystyle
Wilks'_theorem
Ways of computing statistical significance
the null hypothesis. Alternative names are one-sided and two-sided tests; the terminology "tail" is used because the extreme portions of distributions, where
One-_and_two-tailed_tests
Study of what affects viral life spans
counts, a null distribution can be constructed and a p-value computed by comparing the observed transition counts to this null distribution. Beyond the
Viral_phylodynamics
Type of probability distribution
ISBN 978-1-5386-0595-0. Buchanan, K.; et al. (2020). "Null Beamsteering Using Distributed Arrays and Shared Aperture Distributions". IEEE Transactions on Antennas and Propagation
Arcsine_distribution
Statistical method for handling multiple comparisons
discovery rate (FDR) is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. FDR-controlling
False_discovery_rate
British polymath (1890–1962)
determines the best probability distribution that characterizes the system. F-distribution, arises frequently as the null distribution of a test statistic, most
Ronald_Fisher
Epidemiological study design
regression, which is common, can result in biased estimates whose null distribution is different from what is assumed. Ways to account for the random
Nested_case–control_study
Concepts from statistical hypothesis testing
of a true null hypothesis in statistical hypothesis testing. A type II error, or a false negative, is the incorrect acceptance of a false null hypothesis
Type_I_and_type_II_errors
Cluster analysis problem
of squares expected under the null reference distribution of data. The expected value is estimated by simulating null reference data of characteristics
Determining the number of clusters in a data set
Determining_the_number_of_clusters_in_a_data_set
Statistical interpretation with many tests
to use the Poisson distribution as a model for the number of significant results at a given level α that would be found when all null hypotheses are true
Multiple_comparisons_problem
Educational plan
students or even students and teachers (Jackson, 1986). Excluded curriculum or null curriculum: topics or perspectives that are excluded from the curriculum
Curriculum
Statistical paradox
whether θ {\displaystyle \theta } is 0.5 or some other value. That is, our null hypothesis is H 0 : θ = 0.5 , {\displaystyle H_{0}:\theta =0.5,} and the
Lindley's_paradox
Exact statistical hypothesis test
counterfactual) null hypothesis is that all samples come from the same distribution H 0 : F = G {\displaystyle H_{0}:F=G} . Under the null hypothesis, the
Permutation_test
Probability distribution in economics
The Dagum distribution has been extended to model net wealth distribution, accounting for the observed frequencies of negative and null net wealth.
Dagum_distribution
Statistical test that compares goodness of fit
asymptotically to being χ²-distributed if the null hypothesis happens to be true. The finite-sample distributions of likelihood-ratio statistics are generally
Likelihood-ratio_test
Goodness-of-fit measure in statistics
that is the test aims to gauge the compatibility of given data with the null hypothesis that the data is a realization of independent, identically distributed
D'Agostino's_K-squared_test
Statistical method
it increases the p-value and thus reduces the likelihood of rejecting the null hypothesis when it is true. While widely taught in introductory statistics
Yates's correction for continuity
Yates's_correction_for_continuity
Square matrix containing the distances between elements in a set
positive, the null distribution for cosine similarity is the distribution of the dot product of two independent random unit vectors. This distribution has a mean
Distance_matrix
Statistical test
While the finite sample distributions of Wald tests are generally unknown, it has an asymptotic χ2-distribution under the null hypothesis, a fact that
Wald_test
_{i=1}^{n}(m_{i}-{\bar {m}})^{2}\right)}}}} Under the null hypothesis that the data is drawn from a normal distribution, this correlation will be strong, so W ′ {\displaystyle
Shapiro–Francia_test
Statistical methods for comparing samples
null {\displaystyle MDE=z_{\alpha /2}\cdot {\text{SE}}_{\text{null}}} , the statistical power would be only 50% because the alternative distribution is
Two-proportion_Z-test
Statistical model for a binary dependent variable
the optimum error of the null model, and that the difference between these minimum error will follow a chi-squared distribution, with degrees of freedom
Logistic_regression
Model of changes in a sequence over evolutionary time
to assess the performance of phylogenetic methods and generate the null distribution for certain statistical tests in the fields of molecular evolution
Substitution_model
central distribution describes how a test statistic is distributed when the difference tested is null, noncentral distributions describe the distribution of
Noncentral_distribution
Probability distribution generalizing the F-distribution with a noncentrality parameter
statistic in analysis of variance problems when the null hypothesis is false. The noncentral F-distribution is used to find the power function of such a test
Noncentral_F-distribution
Famous randomized experiment
four cups prepared by a given method. The distribution of possible numbers of successes, assuming the null hypothesis is true, can be computed using the
Lady_tasting_tea
probability and statistics Novikov's condition np-chart Null distribution Null hypothesis Null result Nuisance parameter Nuisance variable Numerical data
List_of_statistics_articles
Linguistics concept
classical model such as the distinction of null subjects and null objects. In the classical theory model, empty (or null) DPs can be broken down into four main
Empty_category
Probability distribution
degenerate distribution on a measure space ( E , A , μ ) {\displaystyle (E,{\mathcal {A}},\mu )} is a probability distribution whose support is a null set with
Degenerate_distribution
equal, the distribution of the T 2 {\displaystyle T^{2}} statistic is known to be an F distribution under the null and a noncentral F-distribution under the
Multivariate Behrens–Fisher problem
Multivariate_Behrens–Fisher_problem
α-quantile of the F distribution with k − 1 numerator degrees of freedom and bk − b − t + 1 denominator degrees of freedom. The null hypothesis is rejected
Durbin_test
Random process independent of past history
{\displaystyle \Omega } (up to a null set). The terminology is inconsistent. Given a Markov chain with a stationary distribution that is strictly positive on
Markov_chain
Software for statistical analysis of molecular evolution
to test substitution pattern homogeneity that involves running a null distribution simulation. MEGA requires the user to specify the number of replicates
Molecular Evolutionary Genetics Analysis
Molecular_Evolutionary_Genetics_Analysis
Probability distribution
A ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables
Ratio_distribution
Measure of variation in statistics
findings). By convention, only effects more than two standard errors away from a null expectation are considered "statistically significant", a safeguard against
Standard_deviation
dF(x)=\int _{0}^{1}u_{n}^{2}(t)\,dt.} For all such functionals, their null distribution (under the hypothetical F {\displaystyle F} ) does not depend on F
Khmaladze_transformation
American record label
to include jazz, classical and other genres of recordings. In 1977, Tom Null's Sarabande Records merged with Varèse International to form Varèse Sarabande
Varèse_Sarabande
Generalized function whose value is zero everywhere except at zero
the Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
Power company in Puerto Rico
Luma Energy is a private power company that is responsible for power distribution and power transmission in the Commonwealth of Puerto Rico. It is also
Luma_Energy
Statistical significance test
pointed out by Fisher, this leads under a null hypothesis of independence to a hypergeometric distribution of the numbers in the cells of the table. This
Fisher's_exact_test
Ratio in statistics
t-statistic is used in a t-test to determine whether to support or reject the null hypothesis. It is very similar to the z-score but with the difference that
T-statistic
Hypothetical invisible cosmic material
by orders of magnitude, these direct detection experiments all reported null results for WIMPs across the standard GeV–TeV mass range. As of late 2025
Dark_matter
2014 American film
released direct-to-video in the United States on August 12, 2014, by SP Distribution. A tall Japanese young male with no recollection of his past wakes up
Tekken_2:_Kazuya's_Revenge
Web forum
leaked. Kiwi Farms was founded in 2013 by Joshua Conner Moon (known as "Null" on the website), a former 8chan administrator. It was originally launched
Kiwi_Farms
Lossless data compression software
memory-usage limit. An xz file is a sequence of one or more streams. There may be null bytes (padding) after each stream. The xz format improves on lzma by allowing
XZ_Utils
Statistics named for Richard von Mises
where w(x; F0) is a specified weight function and F0 is a specified null distribution. If w is the identity function then T(Fn) is the well known Cramér–von-Mises
V-statistic
Simple and widely known encryption technique
frequency distribution of the letters. By graphing the frequencies of letters in the ciphertext, and by knowing the expected distribution of those letters
Caesar_cipher
Language in which certain pronouns may sometimes be omitted
both agreement and referential null subjects that are restricted with respect to their distribution. The partial null-subject languages include most Balto-Slavic
Pro-drop_language
Unit of organization for a sequence of speech sounds
special zero consonant to represent a null onset. As an example, in Hangul, the alphabet of the Korean language, a null onset is represented with ㅇ at the
Syllable
Measure of linear correlation
{r}{\sigma _{r}}}=r{\sqrt {\frac {n-2}{1-r^{2}}}}} has a student's t-distribution in the null case (zero correlation). This holds approximately in case of non-normal
Pearson correlation coefficient
Pearson_correlation_coefficient
Mathematical index used in Bayesian statistics
favor of the null hypothesis since in most applied cases it cannot be lower than 50% (see above). In cases that produce posterior distributions that are close
Probability_of_direction
Misinterpretation of statistical significance
two results: either the null hypothesis is rejected (which however does not prove that the null hypothesis is false), or the null hypothesis cannot be rejected
Misuse_of_p-values
Test of normality in frequentist statistics
Samuel Sanford Shapiro and Martin Wilk. The Shapiro–Wilk test tests the null hypothesis that a sample x1, ..., xn came from a normally distributed population
Shapiro–Wilk_test
Statistical test based on the gradient of the likelihood function
While the finite sample distributions of score tests are generally unknown, they have an asymptotic χ2-distribution under the null hypothesis as first proved
Score_test
Scripting language created in 1994
true and zero as false, as in Perl and C++. The null data type represents a variable that has no value; NULL is the only allowed value for this data type
PHP
American independent record label
Celtic music. Founded by Lisa Null and Patrick Sky as Innisfree Records in 1973, the label was initially based in Null's house in New Canaan, Connecticut
Green_Linnet_Records
Norwegian confectionery company
of Norway at https://urn.nb.no/URN:NBN:no-nb_digavis_byavisasandefjord_null_null_20150408_2_51_1 Raastad, Marlin (April 8, 2015). “På vei mot toppen” (in
Hval_Sjokoladefabrikk
Type of substitution cipher
Slidex Solitaire Codes Book Code talker Poem Steganography Bacon Grille Null Cryptanalysis Cryptogram Frequency analysis Index of coincidence (Units:
Pigpen_cipher
Collection of statistical models
The objective random-assignment is used to test the significance of the null hypothesis, following the ideas of C. S. Peirce and Ronald Fisher. This design-based
Analysis_of_variance
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