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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
model likelihood of the saturated model − ln likelihood of fitted model likelihood of the saturated model ) = − 2 ln ( likelihood of null model likelihood
Logistic_regression
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
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)
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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[citation
Latitudinal gradients in species diversity
Latitudinal_gradients_in_species_diversity
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
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
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
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
Method of statistical inference
Bayesian estimation for assessing null values with Bayesian model comparison for hypothesis testing. Two competing models/hypotheses can be compared using
Statistical_hypothesis_test
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
Object with no referenced value or with defined neutral ("null") behavior
computer programming, a null object is an object with no referenced value or with defined neutral (null) behavior. The null object design pattern, which
Null_object_pattern
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
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
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
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
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
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
Extinct species of human
likely acting on archaic variants, and provides an appropriate set of null models for evaluating positive selection on introgressed segments on chromosome
Neanderthal
Fit of a species living under specific environmental conditions
be excluded, and assumption of such randomness can indeed serve as a null-model. – Many physiological and morphological differences between species can
Ecological_niche
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Scientific discipline
a null hypothesis to niche theory. The hypothesis has sparked controversy, and some authors consider it a more complex version of other null models that
Theoretical_ecology
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
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
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
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
large number of randomized matrices; in addition it implements several null models to estimate the significance of nestedness. Bastolla et al. introduced
Nestedness
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
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
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
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
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
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
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
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
Machine instruction that indicates to a computer to do nothing
NOP or null statement if it has no effect. Null statements may be required by the syntax of some languages in certain contexts. In Ada, the null statement
NOP_(code)
Scales used by rail transport models
Rail transport modelling uses a variety of scales (ratio between the real world and the model) to ensure scale models look correct when placed next to
Rail transport modelling scales
Rail_transport_modelling_scales
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
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
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
Concept in mathematical physics
mathematical physics, a null dust solution (sometimes called a null fluid) is a Lorentzian manifold in which the Einstein tensor is null. Such a spacetime can
Null_dust_solution
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
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
Time series statistical test
In statistics, an augmented Dickey–Fuller test (ADF) tests the null hypothesis that a unit root is present in a time series sample. The alternative hypothesis
Augmented_Dickey–Fuller_test
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
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
Order of amphibians
Michael P. L.; Savage, Jay M.; Gorman, George C. (1997). "Tests of null models for amphibian declines on a tropical mountain". Conservation Biology
Frog
Genetic study of ancient Neanderthal DNA
likely acting on archaic variants, and provides an appropriate set of null models for evaluating positive selection on introgressed segments on chromosome
Neanderthal_genetics
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
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
BMap.Tree loop if M is null then // Not already in the map; add it M := (Key => Key, Value => Value, Left => null, Right => null); BMap.Count += 1; else
ParaSail (programming language)
ParaSail_(programming_language)
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
Type of statistical test
from the null hypothesis. Thus, in applied statistics, a portmanteau test provides a reasonable way of proceeding as a general check of a model's match to
Portmanteau_test
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
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
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
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
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