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Topics referred to by the same term
Pairwise testing may refer to: All-pairs testing Pairwise comparison Paired difference test This disambiguation page lists articles associated with the
Pairwise_testing
Software testing method
In computer science, all-pairs testing or pairwise testing is a combinatorial method of software testing that, for each pair of input parameters to a
All-pairs_testing
Topics referred to by the same term
entities to determine which is preferred All-pairs testing, also known as pairwise testing, a software testing method. This disambiguation page lists mathematics
Pairwise
Statistical hypothesis test
particular set of comparisons "pairwise comparisons"-all possible comparisons i.e. Fisher's least significant difference (LSD) test, Tukey's honestly significant
F-test
that pairwise testing from a resource usage perspective could be applied to reveal deadlocks. Software testing Scalability testing Load testing Software
Concurrent_testing
Statistical test for multiple comparisons
other treatment; that is, it applies simultaneously to the set of all pairwise comparisons μ i − μ j , {\displaystyle \mu _{i}-\mu _{j}\ ,} and identifies
Tukey's_range_test
American research software engineer
D. and Czerwonka, J., "An Empirical Study of the Effectiveness of Pairwise Testing", Proceedings of the 2009 International Conference on Software Engineering
James_D._McCaffrey
Non-parametric method for testing whether samples originate from the same distribution
testing. pairwise.wilcox.test(airquality$Ozone, airquality$Month, p.adjust.method = "bonferroni") Pairwise comparisons using Wilcoxon rank sum test data:
Kruskal–Wallis_test
Graphics structure
result in significant performance improvements, the same number of pairwise tests between bounding volumes are still being performed. By arranging the
Bounding_volume_hierarchy
Post-hoc statistical test for pairwise comparisons
rate. Pairwise comparisons: if the omnibus F-test from step 1 is significant, pairwise t-tests are conducted for all pairs of groups. These tests use a
Fisher's least significant difference
Fisher's_least_significant_difference
Sham and Benny Chung-Ying Zee (2016). A fast and powerful W-test for pairwise epistasis testing. Nucleic Acids Research. doi:10.1093/nar/gkw347 http://www2
W-test
Type of location test in statistical analysis
confounding variables by forming "artificial pairs" and performing a pairwise difference test. These artificial pairs are constructed based on additional variables
Paired_difference_test
Multiple comparison procedure
which has a non-significant range. The procedure consists of a series of pairwise comparisons between means. Each comparison is performed at a significance
Duncan's new multiple range test
Duncan's_new_multiple_range_test
Two numbers without shared prime factors
the set is said to be pairwise coprime (or pairwise relatively prime, mutually coprime or mutually relatively prime). Pairwise coprimality is a stronger
Coprime_integers
Group of techniques to detect a particular nucleic acid sequence
acid (DNA and RNA) strands with corresponding sequences stick together in pairwise chains. But each node of the chain is not very sticky, so the double-stranded
Nucleic_acid_test
Statistical methodology
an extension of classical pairwise comparison procedures, including the Wilcoxon rank-sum test and the Mann–Whitney U test, allowing comparisons to incorporate
Generalized pairwise comparisons
Generalized_pairwise_comparisons
Israeli statistician (1945–2013)
Michele; Hochberg, Yosef (1 January 1987). "Sequentially rejective pairwise testing procedures". Journal of Statistical Planning and Inference. 17: 193–208
Yosef_Hochberg
Nonparametric test of the null hypothesis
of the U statistic, which corresponds to the number of wins out of all pairwise contests (see the tortoise and hare example under Examples below). For
Mann–Whitney_U_test
Process of comparing two entities to determine preference
Pairwise comparison generally is any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some
Pairwise comparison (psychology)
Pairwise_comparison_(psychology)
Statistical test
rejected if the test statistic is in the critical region. If the Cochran test rejects the null hypothesis of equally effective treatments, pairwise multiple
Cochran's_Q_test
Statistical hypothesis test
The Wilcoxon signed-rank test is a non-parametric rank test for statistical hypothesis testing used either to test the location of a population based
Wilcoxon_signed-rank_test
Non-parametric statistical test
Grotenhuis (2017) provide an exact test for pairwise comparison of Friedman rank sums, implemented in R. The Eisinga c.s. exact test offers a substantial improvement
Friedman_test
Statistical procedure
of pairwise comparisons. Tukey's and Scheffé's methods allow any number of comparisons among a set of sample means. On the other hand, Dunnett's test only
Dunnett's_test
Statistical analyses that were not specified before the data were seen
categories of post hoc analyses include: Pairwise comparisons: Tests all possible pairs Trend analysis: Tests for linear or quadratic trends across ordered
Post_hoc_analysis
When the occurrence of one event does not affect the likelihood of another
notions of independence need to be distinguished. The events are called pairwise independent if any two events in the collection are independent of each
Independence (probability theory)
Independence_(probability_theory)
Population genetic test statistic
difference between two measures of genetic diversity: the mean number of pairwise differences and the number of segregating sites, each scaled so that they
Tajima's_D
Chance of wrongly rejecting the null hypothesis
outcomes when testing multiple null hypotheses. Suppose we have a number m of null hypotheses, denoted by: H1, H2, ..., Hm. Using a statistical test, we reject
False_positive_rate
Statistical model for pairwise comparisons
The Bradley–Terry model is a probability model for the outcome of pairwise comparisons between items, teams, or objects. Given a pair of items i and j
Bradley–Terry_model
About simultaneous modular congruences
the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1). The theorem
Chinese_remainder_theorem
Statistical test of variance
in power. The first test in a pairwise MCP, such as that of the most disparate means in Tukey's test, is a form of omnibus test all by itself, controlling
Omnibus_test
Database of handwritten digits
half of the test set were taken from NIST's testing dataset. The original creators of the database keep a list of some of the methods tested on it. In their
MNIST_database
Collection of statistical models
hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing in the
Analysis_of_variance
Probability of making type I errors when performing multiple hypotheses tests
when performing multiple hypotheses tests. FWER is a metric that quantifies the risk caused by multiple testing. It's the probability of making one or
Family-wise_error_rate
Genetic process
frequencies to form a genetic map of the gene. Separately, the mutants were tested in pairwise combinations to measure complementation. An analysis of the results
Complementation_(genetics)
occurs after unit testing and before validation testing. Integration testing takes as its input modules that have been unit tested, groups them in larger
Glossary_of_computer_science
Assessment tool
task load index. Many researchers eliminate these pairwise comparisons, though, and refer to the test as "Raw TLX" then. There has been evidence evaluating
NASA-TLX
Term in computer science
multiple objects, a naive approach would require detecting collisions for all pairwise combinations of objects. As the number of objects increases, the number
Collision_detection
Machine learning technique
converting them into pairwise comparisons for prediction purposes. In the online scenario, when human feedback is collected through pairwise comparisons under
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
Methods in computational biology
sequence analysis were based on sequence alignment either global or local, pairwise or multiple sequence alignment. Alignment-based approaches generally give
Alignment-free sequence analysis
Alignment-free_sequence_analysis
Multiple comparison method in statistics
estimates of all possible contrasts among the factor level means, not just the pairwise differences considered by the Tukey–Kramer method. It works on similar
Scheffé's_method
generalised pairwise comparisons (GPC) framework, a generalisation of the theory underpinning the Finkelstein-Schoenfeld test. The Finkelstein-Schoenfeld test and
Win_statistics
Misuse of data analysis
Lastly, a statistical significance test is carried out to see how likely the results are by chance alone (also called testing against the null hypothesis).
Data_dredging
main effect test is nonspecific and will not allow for a localization of specific mean pairwise comparisons (simple effects). A main effect test will merely
Main_effect
Process in bioinformatics that identifies equivalent sites within molecular sequences
to electronic processing, its practical application remains under testing. Pairwise sequence alignment methods are used to find the best-matching piecewise
Sequence_alignment
Nonparametric measure of rank correlation
are incorporated). Stata implementation: spearman varlist calculates all pairwise correlation coefficients for all variables in varlist. MATLAB implementation:
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
univariate polynomial f, of degree n, over a finite field Fq, which has r ≥ 2 pairwise distinct irreducible factors f 1 , … , f r {\displaystyle f_{1},\ldots
Factorization of polynomials over finite fields
Factorization_of_polynomials_over_finite_fields
Group of genes from one parent
parents. Normally these organisms have their DNA organized in two sets of pairwise similar chromosomes. The offspring gets one chromosome in each pair from
Haplotype
Statistical test for multiple comparisons
almost equivalent to two Student t tests testing μ1=μ2 and μ3=μ4 at nominal type I error rate alpha, without multiple testing procedure; therefore the FWER
Newman–Keuls_method
Generalization of the one-dimensional normal distribution to higher dimensions
independent. This implies that any two or more of its components that are pairwise independent are independent. But, as pointed out just above, it is not
Multivariate normal distribution
Multivariate_normal_distribution
Formula on random variables
j=1i<jnCov(Xi,Xj)=∑i,j=1nCov(Xi,Xj). This can be simplified if X1,…,Xn are pairwise independent or just uncorrelated, integrable random variables, each with
Bienaymé's_identity
builds on the development of methods for comparing treatment outcomes using pairwise comparisons. Finkelstein and Schoenfeld (1999) proposed a method for combining
Net_treatment_benefit
Square matrix containing the distances between elements in a set
square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. Depending upon the application involved
Distance_matrix
"Highly entangled" quantum state of 3 or more qubits
Bouwmeester; M. Daniell; H. Weinfurter; A. Zeilinger (2000). "Experimental test of quantum nonlocality in three-photon GHZ entanglement". Nature. 403 (6769):
Greenberger–Horne–Zeilinger state
Greenberger–Horne–Zeilinger_state
Ethnicity in South America
used to infer genetic ancestry in Brazilians with an admixture model. Pairwise estimates of F(st) among the five Brazilian geopolitical regions suggested
Pardo_Brazilians
Statistical measure of a dendrogram's faithfulness to the data
coefficient) is a measure of how faithfully a dendrogram preserves the pairwise distances between the original unmodeled data points. Although it has been
Cophenetic_correlation
Logic problem, AND of pairwise ORs
for solving constraint satisfaction problems with binary variables and pairwise constraints. They apply this technique to a problem of classroom scheduling
2-satisfiability
Area of discrete mathematics
is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices
Graph_theory
Machine learning algorithm
of regression tree can be extended to any kind of object equipped with pairwise dissimilarities such as categorical sequences. Decision trees are among
Decision_tree_learning
Sequencing all the DNA of an individual at once
genomes was already in use in 1979, broader application benefited from pairwise end sequencing, known colloquially as double-barrel shotgun sequencing
Whole_genome_sequencing
disequilibrium, analysis of molecular variance, mismatch distribution, and pairwise difference tests. The software is designed to be able to handle different kinds
Arlequin_(software)
Reasoning for mathematical statements
are pairwise equivalent. In order to prove that the statements φ 1 , … , φ n {\displaystyle \varphi _{1},\ldots ,\varphi _{n}} are each pairwise equivalent
Mathematical_proof
Structure in combinatorial mathematics
pair of elements is found in the same number of blocks and the design is pairwise balanced. For t = 1, each element occurs in the same number of blocks (the
Block_design
Type of human genetic study conducted on twins
the newer methods allow for explicit testing of the role of different pathways and incorporation and testing of complex effects. Results of twin studies
Twin_study
Structured technique for organizing and analyzing complex decisions
it through a series of pairwise comparisons that derive numerical scales of measurement for the nodes. The criteria are pairwise compared against the goal
Analytic_hierarchy_process
Worked example of using the Analytic Hierarchy Process to choose a car
fifteen comparisons for each of the eight covering criteria. When the pairwise comparisons are as numerous as those in our example, specialized AHP software
Analytic hierarchy process – car example
Analytic_hierarchy_process_–_car_example
Fault in a computer system that presents different symptoms to different observers
using multiple general-purpose computers that would communicate through pairwise messaging in order to reach a consensus, even if some of the computers
Byzantine_fault
Alignment of more than two molecular sequences
Multiple sequence alignments require more sophisticated methodologies than pairwise alignments, as they are more computationally complex. Most multiple sequence
Multiple_sequence_alignment
Property of electoral systems
clones competes. The preferences would be: The Kemeny method arranges the pairwise comparison counts in the following tally table: The ranking scores of all
Independence of clones criterion
Independence_of_clones_criterion
Probability distribution
Toby (2011). Evaluation of the suitability of a Zipfian gap model for pairwise sequence alignment (PDF). International Conference on Bioinformatics Computational
Zipf's_law
Large language model family by SpaceXAI
silent rollout (1–14 November 2025) during which SpaceXSI reported blind pairwise evaluations on live traffic and used feedback to refine the model's behavior
Grok_(chatbot)
Type of heuristic technique
bandits, a variant of traditional MAB, where feedback comes in the form of pairwise comparison. Probability matching is a decision strategy in which predictions
Thompson_sampling
Basic circuit in quantum computing
also with n qubits initialized to | 0 ⟩ {\displaystyle |0\rangle } and pairwise CNOT its qubits with the qubits in register A, such that for each p the
Quantum_logic_gate
Paul Hansen at the University of Otago, the PAPRIKA method is based on pairwise comparisons, as illustrated in the accompanying image. An AI assistant
1000minds
Psychometric factor also known as "general intelligence"
tetrad differences, demonstrated by Spearman in 1924. It states that the pairwise products of two sets of correlations are equal–that is, their difference
G_factor_(psychometrics)
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
relies on squared pairwise differences (making it highly sensitive to extreme outliers), the Gini coefficient relies on absolute pairwise differences, making
Coefficient_of_variation
Single-winner electoral system
The Kemeny method is an electoral system that uses ranked ballots and pairwise comparison counts to identify the most popular choices in an election. It
Kemeny_method
described as a model that is used to obtain measurements from any process of pairwise comparison. Examples of such processes are the comparisons of perceived
Law_of_comparative_judgment
Euclidean Wightman distributions
restricted to ordered n-tuples in R d {\displaystyle \mathbb {R} ^{d}} that are pairwise distinct. These functions are called the Schwinger functions (named after
Schwinger_function
the pairwise distances computed, only about 16% will actually be less than or equal to r c {\displaystyle r_{c}} . In other words, 84% of all pairwise distance
Cell_lists
Plot using the dispersal of scattered dots to show the relationship between variables
variables (dimensions) X1, X2, ... , Xk, the scatter plot matrix shows all the pairwise scatter plots of the variables on a single view with multiple scatter plots
Scatter_plot
Axiom of set theory
set X, if the empty set is not an element of X and the elements of X are pairwise disjoint, then there exists a set C such that its intersection with any
Axiom_of_choice
Concept in natural language processing
Other measures calculate the similarity between ontological instances: Pairwise: measure functional similarity between two instances by combining the semantic
Semantic_similarity
Statistical indicators of the deviation of a sample
Alternatives robust estimators have also been developed, such as those based on pairwise differences and biweight midvariance. These robust statistics are particularly
Robust_measures_of_scale
Privacy-focused encrypted messaging app
end-to-end encrypted group chats. The group chat protocol is a combination of a pairwise double ratchet and multicast encryption. In addition to the properties
Signal_(software)
Multi-modular arithmetic
a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the
Residue_number_system
Simultaneous observation and analysis of more than one outcome variable
algorithms to determine a set of synthetic variables that best represent the pairwise distances between records. The original method is principal coordinates
Multivariate_statistics
Field in statistics pertaining to establishing cause and effect
(a variant of the original PC algorithm) and in dynamical systems using pairwise asymmetric inference (a variant of convergent cross mapping). There is
Exploratory_causal_analysis
Problem in computational complexity theory
S} as a bit vector, computing the set S + S {\displaystyle S+S} of all pairwise sums as a discrete convolution using the fast Fourier transform, and finally
3SUM
Statistical method for handling missing data
any further analysis. Listwise deletion affects statistical power of the tests conducted. Statistical power relies in part on high sample size. Because
Listwise_deletion
Rhythmic division of time in spoken language
durations of vowels in adjacent syllables, it is possible to calculate a Pairwise Variability Index (PVI) from measured vowel durations to quantify the differences
Isochrony
Discrete Fourier transform algorithm
Cooley–Tukey, have excellent numerical properties as a consequence of the pairwise summation structure of the algorithms. The upper bound on the relative
Fast_Fourier_transform
Convention for reporting statistical results
multiple hypothesis testing when using the ANOVA and Tukey's range tests. CLD can also be applied following the Duncan's new multiple range test (which is similar
Compact_letter_display
Diagnostic plot of binary classifier ability
classes are (1) average over all pairwise AUC values and (2) compute the volume under surface (VUS). To average over all pairwise classes, one computes the AUC
Receiver operating characteristic
Receiver_operating_characteristic
Healthcare test
protein. Antibodies against a similar target are tested against all other antibodies in the library in a pairwise fashion to see if antibodies block one another's
Epitope_binning
Fundamental theorem in probability theory and statistics
still, they need not be independent, nor even pairwise independent.[citation needed] By the way, pairwise independence cannot replace independence in the
Central_limit_theorem
Statistical measure
compute the n by n distance matrices (aj, k) and (bj, k) containing all pairwise distances a j , k = ‖ X j − X k ‖ , j , k = 1 , 2 , … , n , b j , k = ‖
Distance_correlation
Medical statistical method
estimator b {\displaystyle b} is the median of the absolute values of all pairwise slopes. The original algorithm is rather slow for larger data sets as its
Passing–Bablok_regression
Statistics dataset
with information about the data set ?iris # Create scatterplots of all pairwise combination of the 4 variables in the data set pairs(iris[1:4], main="Iris
Iris_flower_data_set
Theory of logic to account for observations from quantum theory
symbols, this means that for any sequence {Si}i of pairwise-disjoint Borel subsets of R, {φ(Si)}i are pairwise-orthogonal propositions (elements of Q) and φ
Quantum_logic
Character in J. R. R. Tolkien's Middle-earth
the interactions of the characters as fitting the oppositions and other pairwise relationships of Jungian archetypes, recurring psychological symbols proposed
Galadriel
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