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mathematics, for example in the study of statistical properties of graphs, a null model is a type of random object that matches one specific object in some of
Null_model
Statistical model for a binary dependent variable
minimizes ε2 of the fit to the null model, denoted by εφ2 where the φ subscript denotes the null model. It is seen that the null model is optimized by b0=y‾ where
Logistic_regression
Marker used in SQL databases to indicate a value does not exist
database. Introduced by the creator of the relational database model, E. F. Codd, SQL null serves to fulfill the requirement that all true relational database
Null_(SQL)
Statistical theorem
( likelihood for null model likelihood for alternative model ) = 2 ln ( likelihood for alternative model likelihood for null model ) = 2 × [ ln (
Wilks'_theorem
Measure of network community structure
maximization is not statistically consistent, and finds communities in its own null model, i.e. fully random graphs, and therefore it cannot be used to find statistically
Modularity_(networks)
represents the normalized weight of each link in the null model. Consecutively, and based on the null model, we can derive that the normalized weight distribution
Disparity filter algorithm of weighted network
Disparity_filter_algorithm_of_weighted_network
Hypothetical hybrid species
statistically test their own null model of simple speciation before concluding that speciation was complex, and—even if the null model could be rejected—they
Humanzee
Tribe of mammals
statistically test their own null model of simple speciation before concluding that speciation was complex, and—even if the null model could be rejected—they
Hominini
Method of statistical inference
tester. An adequate statistical model may be associated with a failure to reject the null; the model is adjusted until the null is not rejected. The numerous
Statistical_hypothesis_test
Signature pavilion at Expo 2025
null² (Japanese: ヌルヌル, pronounced Nurunuru) was a Signature Pavilion at the Expo 2025 Osaka, Kansai, Japan, held on Yumeshima Island in Osaka. It was produced
Null²
Software package for sequence analysis
Sequences that score significantly better to the profile-HMM compared to a null model are considered to be homologous to the sequences that were used to construct
HMMER
statistically test their own null model of simple speciation before concluding that speciation was complex, and—even if the null model could be rejected—they
Chimpanzee–human last common ancestor
Chimpanzee–human_last_common_ancestor
Statistical test that compares goodness of fit
based on the ratio of their likelihoods. If the more constrained model (i.e., the null hypothesis) is supported by the observed data, the two likelihoods
Likelihood-ratio_test
How often identical letters appear in the same position in two texts
pair, assuming a uniform random distribution of the characters (the "null model"; see below). Thus, this formula gives the ratio of the total number of
Index_of_coincidence
over- or under-represented graphlets with respect to some random graph null model. RGF-distance compares the frequencies of the appearance of all 3-5-node
Graphlets
Statistical test of variance
{\text{likelihood under fitted model if null hypothesis is true}}{\text{likelihood under saturated model}}}} While the saturated model is a model with a theoretically
Omnibus_test
Theory of evolutionary biology
controversy, and some authors consider it a more complex version of other null models that fit the data better. "Neutrality" means that at a given trophic
Unified neutral theory of biodiversity
Unified_neutral_theory_of_biodiversity
American evolutionary ecologist and biogeographer
informatics. Biogeographical null models. With co-author David Winkler, Colwell developed one of the first biogeographical null models incorporating simulated
Robert_K._Colwell
Ratio of competing statistical models
parameters, such as a null hypothesis and an alternative, but this is not necessary; for instance, it could also be a non-linear model compared to its linear
Bayes_factor
large number of randomized matrices; in addition it implements several null models to estimate the significance of nestedness. Almeida-Neto et al introduced
Nestedness
Statistical measure of fit
the model being fitted and the null model, respectively, \ln denotes the natural logarithm, and n is the number of observations. L0 is the model with
Pseudo-R-squared
Statistical hypothesis test
model i. If the regression model has been calculated with weights, then replace RSSi with χ2, the weighted sum of squared residuals. Under the null hypothesis
F-test
Measure of the quantity of an introduced species
Colautti et al. (2006), proposes that propagule pressure should act as a null model for studies that consider/compare processes of invasions to patterns of
Propagule_pressure
Instrument to measure minute voltage
A null detectors is an electrical measurement instrument used to measure minute voltages. High precision null detectors can resolve voltage differences
Null_detector
Searching for wild food resources
and 1970s. Their goal was to quantify and formalize a set of models to test their null hypothesis that animals forage randomly. Important contributions
Foraging
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
Global increase in species richness from polar regions to tropics
mid-domain models attempt to exclude any direct environmental or evolutionary influences on species richness, they have been claimed to be null models. On this
Latitudinal gradients in species diversity
Latitudinal_gradients_in_species_diversity
Misinterpretation of statistical significance
alone. The p-value is computed under the assumption that a certain model, usually the null hypothesis, is true. This means that the p-value is a statement
Misuse_of_p-values
Family of random graph models
Configuration Models provide a null hypothesis for understanding the role of degree distributions in shaping network properties. Configuration Models can be
Configuration_model
Form of statistical factor analysis
chi-square for the hypothesized model to one from a “null”, or “baseline” model. This null model almost always contains a model in which all of the variables
Confirmatory_factor_analysis
Technique using a large language model as an evaluator
Tianyu; Du, Chao; et al. (2025). Cheating Automatic LLM Benchmarks: Null Models Achieve High Win Rates. The Thirteenth International Conference on Learning
LLM-as-a-Judge
Function of the observed sample results
In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed,
P-value
Database model
three-valued logic (True, False, Missing/NULL) version of it to deal with missing information, and in his The Relational Model for Database Management Version
Relational_model
Study of collection and analysis of data
idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, an alternative to an idealized null hypothesis
Statistics
property of being maximally unbiased null models for network inference (e.g. biological network inference). Each model defines a family of probability distributions
Maximum-entropy random graph model
Maximum-entropy_random_graph_model
Observed inability to reproduce scientific studies
are presented here. In the most common case, null hypothesis testing, there are two hypotheses, a null hypothesis H 0 {\displaystyle H_{0}} and an alternative
Replication_crisis
Ratio estimating the balance between nonsynonymous and synonymous substitutions
distinguish between a null model (Ka/Ks = 1) and the observed results. The Ka/Ks ratio is a more powerful test of the neutral model of evolution than many
Ka/Ks_ratio
Computer fault caused by access to restricted memory
error in programs written in languages that support pointers that can be null, or that can be set to an arbitrary value, or that support arrays, and in
Segmentation_fault
Type of sub-graph
interchangeably. There is an ensemble Ω(G) of random graphs corresponding to the null-model associated to G. We should choose N random graphs uniformly from Ω(G)
Network_motif
Speciation that occurs between geographically isolated populations
complexity of speciation. Allopatry is often regarded as the default or "null" model of speciation, but this too is debated. Reproductive isolation acts as
Allopatric_speciation
Brackish lake on the Altiplano in Chile
October 2021. De los Ríos-Escalante, Patricio (27 February 2011). "A null model to study community structure of microcrustacean assemblages in Northern
Laguna_Miscanti
Statistical Markov model
In probability theory, a hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or hidden) Markov process (referred
Hidden_Markov_model
Statistical hypothesis test
test is valid when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof
Chi-squared_test
Concept in relational databases
and non-null primary key value; this is the same as saying that each row in a table represents a single instance of the entity type modelled by the table
Entity_integrity
Statistical property of measurement
Modeling. 9 (2): 233–255. doi:10.1207/s15328007sem0902_5. S2CID 32598448. Widaman, Keith F.; Thompson, Jane S. (2003-03-01). "On specifying the null model
Measurement_invariance
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
American model and actress (born 1956)
July 2, 1956) is an American model and actress. She began modeling in the 1970s and became one of the most sought-after models in the world. She transitioned
Jerry_Hall
Concept in ecology
be excluded, and assumption of such randomness can indeed serve as a null-model. – Many physiological and morphological differences between species can
Ecological_niche
Concept in graph theory
or even distinguish the graph from one generated by a null model such as the Erdos–Renyi model without community structure. This transition is independent
Community_structure
Danish botanist (1860–1938)
spectrum" (Raunkiær 1918 – see below). Thereby, he devised the first null model in the history of ecology. Raunkiær was a keen naturalist, who described
Christen_C._Raunkiær
Immunodeficient laboratory mice brand
Activating Gene-1 (NOD- Rag 1 null ) Interleukin (IL)-2 Receptor Common Gamma Chain ( IL 2 Rγ null ) Null Mice: A Radioresistant Model for Human Lymphohaematopoietic
NSG_mouse
Concepts underlying statistical methods
and the probability of exceeding that statistic under a default or 'null' model is compared to a threshold. The threshold (the numeric version of "sufficiently
Foundations_of_statistics
Polish American mathematician (1894–1981)
Fisher’s formulation of the null hypothesis. Fisher had emphasized significance testing as a measure of evidence against a null model, but Neyman and Pearson
Jerzy_Neyman
Diagnostic plot of binary classifier ability
S2CID 23054670. Karplus, Kevin (2011); Better than Chance: the importance of null models, University of California, Santa Cruz, in Proceedings of the First International
Receiver operating characteristic
Receiver_operating_characteristic
if the sample statistics are significantly different from the assumed null-model. True values of a population, which are unknowable in practice, are called
Statistical_proof
American 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
Obligation on a party in a dispute to provide sufficient warrant for their position
can be done without a null hypothesis, by specifying a statistical model corresponding to each candidate hypothesis and using model selection techniques
Burden_of_proof_(philosophy)
Syntax for defining data structures
first_name VARCHAR(50) not null, last_name VARCHAR(75) not null, mid_name VARCHAR(50) not null, dateofbirth DATE not null ); Some forms of CREATE TABLE
Data_definition_language
inhomogeneities may be occurring. The null model for point patterns is complete spatial randomness (CSR), modeled as a Poisson process in Rn, which implies
Point_pattern_analysis
Multivariate statistical technique
of other (usually environmental) variables; this allows testing of a null model by Monte-Carlo permutation analysis. The example shows an ideal data set:
Detrended correspondence analysis
Detrended_correspondence_analysis
Infinite cardinal number
ℵ 0 {\displaystyle \aleph _{0}} (read aleph-nought, aleph-zero, or aleph-null); the next larger cardinality of a well-ordered set is ℵ 1 , {\displaystyle
Aleph_number
Discussion of the meaning and usage of the terms evolution, fact and theory
neutral theory of molecular evolution is used to study evolution as a null model against which tests for natural selection can be applied. The following
Evolution_as_fact_and_theory
Milenković, Ioannis Filippis, Michael Lappe, and Nataša Pržulj, Optimized Null Model for Protein Structure Networks, 2009, PLOS One 4(6): e5967. http://bio-nets
GraphCrunch
a method that they developed, that of "null" models, to be used much in the way that all scientists use null hypotheses to verify that their results
History_of_ecology
Lake and volcano in Chile
that time. Ríos, Patricio De Los; Gajardo, Gonzalo (1 July 2010). "A Null Model to Explain Zooplankton Species Associations in Saline Lakes of the South
Laguna_Miñiques
Measure of connection disorder in a network
know the adjacency matrix). On the other hand, this ensemble serves as a null model when the actual microscopic configuration of the network is known, allowing
Network_entropy
Subfield of genealogy
the branching patterns in the molecular trees. This study rejected the null model and found that the origin for all extant Amazonian poison frog species
Phylogeography
Relational database programming language
follow standards. In particular, date and time syntax, string concatenation, NULLs, and comparison case sensitivity vary from vendor to vendor. PostgreSQL
SQL
Statistical test comparing two probability distributions
distribution functions of two samples. The null distribution of this statistic is calculated under the null hypothesis that the sample is drawn from the
Kolmogorov–Smirnov_test
Method of result aggregation from multiple clustering algorithms
GAP-statistic. However, these methods rely on certain assumptions for the null model that may not always be appropriate. Şenbabaoğlu et al demonstrated the
Consensus_clustering
Rohde, K. (2002). "Co-occurrence of ectoparasites of marine fishes: a null model analysis". Ecology Letters. 5 (1): 86–94. Bibcode:2002EcolL...5...86G
Vacant_niche
Relational database design
primary key value and column name. Rule 3: Systematic treatment of null values: Null values (distinct from the empty character string or a string of blank
Codd's_12_rules
Concepts from statistical hypothesis testing
a true null hypothesis in statistical hypothesis testing. A type II error, or a false negative, is the incorrect failure to reject a false null hypothesis
Type_I_and_type_II_errors
Ecological integrity assessment
Matthews, Jeffrey W.; Spyreas, Greg; Long, Colleen M. (May 2015). "A null model test of Floristic Quality Assessment: Are plant species' Coefficients
Floristic_Quality_Assessment
modeled using a nullor, and the textbook analysis of a feedback circuit using an ideal op-amp uses the mathematical conditions imposed by the nullor to
Nullor
Methods in evolutionary biology
JSTOR 2992503. Gittleman, J. L.; Kot, M. (1990). "Adaptation: statistics and a null model for estimating phylogenetic effects". Systematic Zoology. 39 (3): 227–241
Phylogenetic comparative methods
Phylogenetic_comparative_methods
Type of data model
An entity–attribute–value model (EAV) is a data model optimized for the space-efficient storage of sparse—or ad-hoc—property or data values, intended
Entity–attribute–value_model
American ecologist and professor
paradigm of competitively structured communities, championing the use of null models in community ecology. Debate on the subject in the ecological literature
Daniel_Simberloff
Statistical interpretation with many tests
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.[citation
Multiple_comparisons_problem
Model of electrical conduction
The Drude model or the Drude–Lorentz model of electrical conduction in metals was proposed in 1900 by Paul Drude, and refined by Hendrik Lorentz in 1905
Drude_model
trophically coherent (or incoherent) can be investigated by comparison with a null model. This is provided by the basal ensemble, which comprises networks in which
Trophic_coherence
German biologist
2002 with N J Gotelli. Co-occurrence of ectoparasites of marine fishes: null model analysis. Ecology Letters, 5, 86–94. 2002 Ecology and biogeography of
Klaus_Rohde
Method in molecular biology
of interaction (initial spline fitting, aka spline-1) and refining the null model (spline-2). The result of Fit-Hi-C is a list of pairwise intra-chromosomal
Chromosome conformation capture
Chromosome_conformation_capture
Species delimitation method in molecular systematics
species. The model identifies a "threshold" time point where there is a significant shift in branching rates. It compares a null model, in which a single
General mixed Yule–coalescent model
General_mixed_Yule–coalescent_model
Form of causal modeling that fit networks of constructs to data
for each model degree of freedom, doesn't that mean that people testing models with null-hypotheses of non-zero RMSEA are doing deficient model testing
Structural_equation_modeling
Networks with multiple kinds of relations
i α {\displaystyle P_{j\beta }^{i\alpha }} is the tensor encoding the null model and the value of components of S a i α {\displaystyle S_{a}^{i\alpha }}
Multidimensional_network
Evolutionary theory
with a solid theoretical core, null hypotheses need to be incorporated and alternatives need to falsify the null model before being accepted. Otherwise
Constructive neutral evolution
Constructive_neutral_evolution
Genetic technique for identifying organisms in mixed samples
PMID 17576602. S2CID 4219676. Vázquez, Diego P.; Aizen, Marcelo A. (2003). "Null Model Analyses of Specialization in Plant–Pollinator Interactions". Ecology
Metabarcoding
Mathematical model for data types
In computer science, an abstract data type (ADT) is a mathematical model for data types, defined by its behavior (semantics) from the point of view of
Abstract_data_type
Swiss botanist and plant geographer (1880–1960)
analysis and mathematics. For instance, he made one of the earliest null models in biogeography showing that - in records of plant or animal species
Arthur_Maillefer
Standardized AI performance test
A language model benchmark is a standardized test designed to evaluate the performance of language models on various natural language processing tasks
Language_model_benchmark
Study of angle-preserving transformations of a geometric space
the model flat geometry is defined analogously as the homogeneous space O(p + 1, q + 1) / H, where H is again taken as the stabilizer of a null line
Conformal_geometry
Evolution theory has become the null model against which tests for selection are based, and divergence from this model can be explained by directional
HKA_test
Values that a data element may contain
have one of two known code values: "M" for married, "S" for single, and NULL for records where marital status is unknown or not applicable. The data domain
Data_domain
Concept in statistics
In statistics, a latent class model (LCM) is a model for clustering multivariate discrete data. It assumes that the data arise from a mixture of discrete
Latent_class_model
Technique in mathematical modeling
equations) it is possible to have a null approximation error, resulting in an exact model order reduction. Contemporary model order reduction techniques can
Model_order_reduction
Statistical hypothesis test
in which the test statistic follows a Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow
Student's_t-test
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
Database management system
Customers ( Id CHAR(12) NOT NULL PRIMARY KEY, Surname VARCHAR(32) NOT NULL, FirstName VARCHAR(32) NOT NULL, DOB DATE NOT NULL # DOB: Date of Birth ); SELECT
Object–relational_database
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
travel, tourism, insurance
NULL MODEL
NULL MODEL
Surname or Lastname
English
English : from the Old English personal name Cula.Americanized spelling of German and Swedish Kall or German Koll.
Girl/Female
Greek American English French
Shining light. The bright one.
Surname or Lastname
English
English : from an Old English personal name, Lulla.German (Lüll) : from a short form of any of the Germanic personal names formed with liut- ‘people’ as the first element.Catalan (also Llull) : from the personal name Lullus, probably of Germanic origin.
Girl/Female
American, Australian, British, Danish, English, French, German, Greek, Irish, Swedish
Shining Light; Light; The Light of the Sun from Eleanor and Variation of Helen; Sun Ray; Stone; Champion; Horn; Torch; Moon; Moon Elope
Boy/Male
Hindu
Battle maiden
Girl/Female
Arabic
Arabian Jasmine
Boy/Male
British, English, Spanish
Strong Leader; Empty
Surname or Lastname
English
English : unexplained.Possibly a shortened form of any of several German compound surnames formed with Full- or Füll-.
Boy/Male
Shakespearean
Love's Labours Lost' A constable.
Male
Hungarian
Hungarian form of Greek Emmanouel, EMÃNUEL means "God is with us."
Female
English
Pet form of English Eleanor, NELL means "foreign; the other."
Male
English
Medieval pet form of English Oliver, probably NOLL means "elf army."
Boy/Male
British, English
Grinder
Boy/Male
Celtic
Champion.
Surname or Lastname
Dutch and German
Dutch and German : from the personal name Nel, a reduced form of Cornelius.South German : nickname from Middle High German nelle ‘crown of the head’, perhaps denoting an obstinate person.English : from the Middle English personal name Nel(le), a variant of Neill.
Girl/Female
Afghan, Australian, Danish, Swedish
God
Surname or Lastname
English
English : nickname from Middle English gulle ‘gull’ or gul(le) (Old Norse gulr) ‘yellow’, ‘pale’ (of hair or complexion).Swiss German : nickname for an irascible or unreliable person, from an Alemannic form of Latin gallus ‘rooster’. See also Guell.
Surname or Lastname
English
English : nickname for a strong, aggressive, bull-like man, from Middle English bul(l)e, bol(l)e. Occasionally, the name may denote a keeper of a bull. Compare Bulman.German (mainly northern) : from a byname for a cattle breeder, keeper, or dealer. Compare South German Ochs.South German : nickname for a short fat man, a variant of Bolle, or a nickname for a man with the physical characteristics of a bull.
Surname or Lastname
English
English : of uncertain origin, possibly from an unrecorded late survival of the Old English personal name Tula.South German (Tüll) : from a nickname for someone who was patient, from Middle High German dult ‘patience’; or from a personal name formed with the same word; or from Middle High German tult, dult ‘fair’, ‘festival’ (Bavarian Dult).South German : nickname for a stubborn man, Tull.Altered spelling of German Toll.
Surname or Lastname
English
English : variant of Hill 1.English : from a pet form of Hugh.
NULL MODEL
NULL MODEL
NULL MODEL
NULL MODEL
NULL MODEL
NULL MODEL
NULL MODEL
a.
Full to the brim; quite full; chock-full.
a.
No; not any; as, nul disseizin; nul tort.
v. i.
To become dull or stupid.
v. t.
To heat, sweeten, and enrich with spices; as, to mull wine.
n.
A knob, handle, or lever, etc., by which anything is pulled; as, a drawer pull; a bell pull.
Compar.
Not wanting in any essential quality; complete, entire; perfect; adequate; as, a full narrative; a person of full age; a full stop; a full face; the full moon.
v. t.
To strip off or separate the hull or hulls of; to free from integument; as, to hull corn.
n.
The act of rowing; as, a pull on the river.
v. t.
To move or operate by the motion of drawing towards one; as, to pull a bell; to pull an oar.
n.
A contest; a struggle; as, a wrestling pull.
n.
A promontory; as, the Mull of Cantyre.
a.
Quite full; choke-full.
Compar.
Abundantly furnished or provided; sufficient in. quantity, quality, or degree; copious; plenteous; ample; adequate; as, a full meal; a full supply; a full voice; a full compensation; a house full of furniture.
superl.
Not bright or clear to the eye; wanting in liveliness of color or luster; not vivid; obscure; dim; as, a dull fire or lamp; a dull red or yellow; a dull mirror.
superl.
Furnishing little delight, spirit, or variety; uninteresting; tedious; cheerless; gloomy; melancholy; depressing; as, a dull story or sermon; a dull occupation or period; hence, cloudy; overcast; as, a dull day.
a.
Of or pertaining to a bull; resembling a bull; male; large; fierce.
v. t.
To gather with the hand, or by drawing toward one; to pluck; as, to pull fruit; to pull flax; to pull a finch.
v. t.
To endeavor to raise the market price of; as, to bull railroad bonds; to bull stocks; to bull Lake Shore; to endeavor to raise prices in; as, to bull the market. See 1st Bull, n., 4.
n.
A cully; a dupe; a gull. See Cully.
v. t.
To dispirit or deaden; to dull or blunt.
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