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Concept in statistical analysis
Bivariate analysis is one of the simplest forms of quantitative (statistical) analysis. It involves the analysis of two variables (often denoted as X, Y)
Bivariate_analysis
Type of statistics
differentiating univariate and bivariate analysis is that bivariate analysis is not only a simple descriptive analysis, but also it describes the relationship
Descriptive_statistics
Topics referred to by the same term
indeterminates Bivariate data, that shows the relationship between two variables Bivariate analysis, statistical analysis of two variables Bivariate distribution
Bivariate
Generalization of the one-dimensional normal distribution to higher dimensions
the vector of [XY] ′ {\displaystyle {\text{[XY]}}\prime } is bivariate normal. The bivariate iso-density loci plotted in the x , y {\displaystyle x,y} -plane
Multivariate normal distribution
Multivariate_normal_distribution
Statistical method that summarizes and/or integrates data from multiple sources
AS, Rutjes AWS, Scholten RJPM, Bossuyt PMM, Zwinderman AH (2005). Bivariate analysis of sensitivity and specificity produces informative summary measures
Meta-analysis
Simultaneous observation and analysis of more than one outcome variable
correlation analysis finds linear relationships among two sets of variables; it is the generalised (i.e. canonical) version of bivariate correlation.
Multivariate_statistics
Topics referred to by the same term
Variable analysis may refer to: Bivariate analysis Multivariate analysis Univariate analysis This disambiguation page lists articles associated with the
Variable_analysis
analyses can be used during the initial data analysis phase: Univariate statistics (single variable) Bivariate associations (correlations) Graphical techniques
Data_analysis
Non-parametric statistic on information transfer
using a non-uniform embedding. While it was originally defined for bivariate analysis, transfer entropy has been extended to multivariate forms, either
Transfer_entropy
Measure of linear correlation
behavior of the correlation estimate. A stratified analysis is one way to either accommodate a lack of bivariate normality, or to isolate the correlation resulting
Pearson correlation coefficient
Pearson_correlation_coefficient
Statistical term of data on each of two paired variables
In statistics, bivariate data is data on each of two variables, where each value of one of the variables is paired with a value of the other variable
Bivariate_data
Type of data measuring one attribute
distribution Bivariate analysis Multivariate analysis List of probability distributions Kachigan, Sam Kash (1986). Statistical analysis: an interdisciplinary
Univariate_(statistics)
Set of statistical processes for estimating the relationships among variables
X_{1i},X_{2i})} . Suppose further that the researcher wants to estimate a bivariate linear model via least squares: Y i = β 0 + β 1 X 1 i + β 2 X 2 i + e
Regression_analysis
1986 United States Supreme Court case
lower court correctly relied only on an ecological regression and bivariate analysis. Justice White wrote separately to note that he disagreed with Justice
Thornburg_v._Gingles
Method of analysing a dynamical system
S2CID 255630484. Marwan, N., Kurths, J. (2002). "Nonlinear analysis of bivariate data with cross recurrence plots". Physics Letters A. 302 (5–6):
Recurrence quantification analysis
Recurrence_quantification_analysis
Statistical distribution for dependence between random variables
Haq, M.S. (1978). "A class of bivariate distributions including the bivariate logistic". Journal of Multivariate Analysis. 8 (3): 405–412. Bibcode:1978JMA
Copula_(statistics)
binary digits 0 and 1. binomial distribution bivariate analysis A type of quantitative statistical analysis in which exactly two variables are analyzed
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Association of one output to each input
graph of a bivariate surface over a two-dimensional real domain may be interpreted as defining a parametric surface, as used in, e.g., bivariate interpolation
Function_(mathematics)
Discrete probability distribution
increasing or decreasing. This distribution has been extended to the bivariate case. The generating function for this distribution is g ( u , v ) = exp
Poisson_distribution
Thematic map visualizing multiple variables
A bivariate map or multivariate map is a type of thematic map that displays two or more variables on a single map by combining different sets of symbols
Multivariate_map
Sequence of data points over time
of non-stationarity) Bivariate linear measures Maximum linear cross-correlation Linear Coherence (signal processing) Bivariate non-linear measures Non-linear
Time_series
Birnbaum–Saunders distribution Birth–death process Bispectrum Bivariate analysis Bivariate von Mises distribution Black–Scholes Bland–Altman plot Blind
List_of_statistics_articles
Method for analyzing stability of slopes of soil or rock
probability of slope failure induced by rainfall at a specific slope using bivariate distribution of rainfall intensity and duration". Engineering Geology
Slope_stability_analysis
Nonparametric spectral estimation method
have a unit root but are cointegrated. The application of SSA in this bivariate framework produces a smoothed series of the common root component. The
Singular_spectrum_analysis
Statistical phenomenon
identical marginal distributions with mean μ. In this formalization, the bivariate distribution of X1 and X2 is said to exhibit regression toward the mean
Regression_toward_the_mean
Multivariable generalization of the Student's t-distribution
standard but not the only choice. An important special case is the standard bivariate t-distribution, p = 2: f ( t 1 , t 2 ) = | A | 1 / 2 2 π ( 1 + ∑ i , j
Multivariate_t-distribution
Type of mathematical expression
multivariate polynomial. A polynomial with two indeterminates is called a bivariate polynomial. These notions refer more to the kind of polynomials one is
Polynomial
Branch of statistics focusing on large deviations
Walker, S. J.; Gallagher, P. T.; Bowers, C. F. (May 2025). "Bivariate Extreme Value Analysis for Space Weather Risk Assessment: Solar Wind—Magnetosphere
Extreme_value_theory
Graphical tool in probability
trees, and are themselves specializations of Cantor tree. Combined with bivariate copulas, regular vines have proven to be a flexible tool in high-dimensional
Vine_copula
German-American cyberneticist (1932–2022)
Situations, Ph.D. Dissertation, Urbana: University of Illinois, 400 pp. 1970, "Bivariate agreement coefficients for reliability of data", in E. F. Borgatta: Sociological
Klaus_Krippendorff
Concept in mathematical modeling, statistical modeling and experimental sciences
independent variable and Y as the dependent variable. This is also called a bivariate dataset, (x1, y1)(x2, y2) ...(xi, yi). The simple linear regression model
Dependent and independent variables
Dependent_and_independent_variables
Table that displays the frequency of variables
theory of evolution. Dulau and Co. Ferguson, G. A. (1966). Statistical analysis in psychology and education. New York: McGraw–Hill. Smith, S. C., & Albaum
Contingency_table
Field in statistics pertaining to establishing cause and effect
Causal analysis is the field of experimental design and statistical analysis pertaining to establishing cause and effect. Exploratory causal analysis (ECA)
Exploratory_causal_analysis
Branch of statistics mathematics
{\displaystyle \mathbb {E} (Y|X)=\mathbb {E} (Y)+\int _{0}^{1}g(t,X(t))dt} for a bivariate smooth additive surface g : [ 0 , 1 ] × R ⟶ R {\displaystyle g:[0,1]\times
Functional_data_analysis
Interpolation on functions of more than one variable
or defined over a multi-dimensional domain. A common special case is bivariate interpolation or two-dimensional interpolation, based on two variables
Multivariate_interpolation
Characteristic property of holomorphic functions
complex functions. The equations are and where u(x, y) and v(x, y) are real bivariate differentiable functions. Typically, u and v are the real and imaginary
Cauchy–Riemann_equations
Topics referred to by the same term
computing Multivariate analysis Multivariate random variable Multivariate regression Multivariate statistics Univariate Bivariate (disambiguation) This
Multivariate
Statistical relationship
is a type of statistical relationship between two random variables or bivariate data. It usually refers to the extent to which a pair of quantities are
Correlation
Nonparametric measure of rank correlation
{\displaystyle \ n\ } is the number of observations. [Proof] Consider a bivariate sample ( X i , Y i ) , i = 1 , … n {\displaystyle \ (X_{i},Y_{i})\
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Numerical measure of a statistical relationship between variables
as ordered-category variables. The two continuous variables followed a bivariate normal distribution. When both variables are dichotomous instead of ordered-categorical
Correlation_coefficient
making it a robust tool for effective connectivity analysis. Comparison of performance of bivariate and multivariate estimators of connectivity may be
Brain_connectivity_estimators
Real function with secant line between points above the graph itself
(2002). Convex Analysis in General Vector Spaces. World Scientific. ISBN 9812380671. H. Bauschke and P. L. Combettes (2011). Convex Analysis and Monotone
Convex_function
Statistical method for genetic variance component estimation
quantifying the contribution of non-additive/non-linear effects of SNPs; and bivariate analyses of multiple phenotypes to quantify their genetic covariance (co-heritability
Genome-wide complex trait analysis
Genome-wide_complex_trait_analysis
Representation of a mathematical function
Foundations of Real and Abstract Analysis. Springer. p. 285. ISBN 0-387-98239-6. Zălinescu, Constantin (30 July 2002). Convex Analysis in General Vector Spaces
Graph_of_a_function
Formal power series
m z n {\displaystyle F(s,t):=\sum _{m,n\geq 0}f(m,n)w^{m}z^{n}} is a bivariate rational generating function, then its corresponding diagonal generating
Generating_function
Statistical method for analysing climate data
assumed to follow a bivariate normal distribution The ellipse shows a single contour of probability density from this bivariate normal, with higher values
Directional component analysis
Directional_component_analysis
Stability of soil or rock slopes
probability of slope failure induced by rainfall at a specific slope using bivariate distribution of rainfall intensity and duration". Engineering Geology
Slope_stability
American statistician and defense acquisitions analyst
University, with the dissertation Two statistical problems involving the bivariate normal distribution arising from legal issues. In 1983 she moved to the
Nancy_Spruill
Statistical transformation
variance that is stable over different values of r. Given a set of N bivariate sample pairs (Xi, Yi), i = 1, ..., N, the sample correlation coefficient
Fisher_transformation
Statistical technique
David I.; Wright, Ian J.; Falster, Daniel S.; Westoby, Mark (2006). "Bivariate line-fitting methods for allometry". Biological Reviews. 81 (2): 259–291
Total_least_squares
Test statistic
(for the geometric mean age) space, or if the compositional data fit a bivariate normal distribution in [log(U/He),log(Th/He)]-space (for the central age)
Reduced_chi-squared_statistic
British eugenist, polymath, and behavioural geneticist (1822–1911)
discovered the properties of the bivariate normal distribution and its relationship to correlation and regression analysis. In 1846, the French physicist
Francis_Galton
Statistical test
1093/biomet/36.3-4.317. Rebecca M. Warner (2013). Applied Statistics: From Bivariate Through Multivariate Techniques. SAGE. p. 778. ISBN 978-1-4129-9134-6
Box's_M_test
Probability distribution
the probability distribution of the magnitude of a circularly symmetric bivariate normal random variable, possibly with non-zero mean (noncentral). It was
Rice_distribution
Statistical concept
pattern analysis routine is used to generate multivariate tail-dependencies consistent with a set of univariate and (in some sense) bivariate moments
Mixture_model
Family of distributions that generalize the multivariate normal distribution
used in classical multivariate analysis, while elliptical distributions are used in generalized multivariate analysis, for the study of symmetric distributions
Elliptical_distribution
Polish statistician
analysis. Dabrowska's estimator, from her paper "Kaplan–Meier estimate on the plane" (Annals of Statistics, 1988) is a widely used tool for bivariate
Dorota_Dabrowska
Concept in statistics
urban analysis, implements kernel density estimation through kernel_smoothing. In SAS, proc kde can be used to estimate univariate and bivariate kernel
Kernel_density_estimation
Data visualization
JSTOR 2685133. Rousseeuw, P. J.; Ruts, I.; Tukey, J. W. (1999). "The Bagplot: A Bivariate Boxplot". The American Statistician. 53 (4): 382–387. doi:10.2307/2686061
Box_plot
Statistical modeling method
conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution
Linear_regression
Mathematical idealization of the surface of a body
the parameters. Let z = f(x, y) be a function of two real variables, a bivariate function. This is a parametric surface, parametrized as x = t y = u z
Surface_(mathematics)
Mathematical analysis technique
\sigma _{1,2}}\right)\,\,\,\,\,\,\,a,b\,\,{\rm {constants}}} NOTES: BVN is bivariate Normal PDF. “n” is the sample size. Type I bias, absolute............
Experimental uncertainty analysis
Experimental_uncertainty_analysis
Plot using the dispersal of scattered dots to show the relationship between variables
plots from line charts is the representation of specific observations of bivariate data where one variable is plotted on the horizontal axis and the other
Scatter_plot
Area in which an animal lives and moves
methods for constructing utilization distributions are the so-called bivariate Gaussian or normal distribution kernel density methods. More recently
Home_range
Involving a single variable
how similar or different the data are scattered. Arity Bivariate Multivariate Univariate analysis Univariate binary model Univariate distribution Grünwald
Univariate
American ecologist (1920–1980)
temperature and mean annual precipitation. By plotting these two metrics on a bivariate graph, he successfully mapped the boundaries of major vegetation types
Robert_Whittaker_(ecologist)
In statistics, a measurement of the agreement between two variables
4780132310. PMID 7701147. Klaus Krippendorff (1970). E. F. Borgatta (ed.). "Bivariate Agreement Coefficients for Reliability of Data". Sociological Methodology
Concordance correlation coefficient
Concordance_correlation_coefficient
Function of observations and unobservable parameters
vectors ( X i , Y i ) ′ {\displaystyle (X_{i},Y_{i})'} is taken from a bivariate bivariate normal distribution with unknown correlation ρ {\displaystyle \rho
Pivotal_quantity
Measure of covariance of components of a random vector
different assets that investors should (in a normative analysis) or are predicted to (in a positive analysis) choose to hold in a context of diversification
Covariance_matrix
Method used in sports betting
distribution model, same as Maher (1982). Bivariate Poisson distribution model that uses generalisation of bivariate Poisson distribution that allows negative
Statistical association football predictions
Statistical_association_football_predictions
{\displaystyle f_{0}} . Going further into higher interactions, the next stop is bivariate functions f i j ( x i , x j ) {\displaystyle f_{ij}(x_{i},x_{j})} which
High-dimensional model representation
High-dimensional_model_representation
Certain type of mathematics from secondary school onwards
or teacher) from a list of four. The core modules are Univariate Data, Bivariate Data, Time Series, Number Patterns and Business-Related Mathematics. The
Further_Mathematics
Mathematical curve outputted from a specific pair of parametric equations
points, at which a function may be sampled in order to compute either a bivariate interpolation or quadrature of the function over the domain [−1,1] × [−1
Lissajous_curve
Indian statistician (1915–1996)
characterization of classical bivariate normal distribution through normal conditional distributions. Normal conditional distributions are bivariate continuous probability
Anil_Kumar_Bhattacharyya
latent variable Y ∗ {\displaystyle Y^{*}} is used. In contrast, in the bivariate probit model there are two binary dependent variables Y 1 {\displaystyle
Multivariate_probit_model
Statistical hypothesis test
size are described at these websites. Power Analysis for Two-group Independent sample t-test | R Data Analysis Examples G*Power Ps Commercial software packages
Student's_t-test
Statistical model
the sources of the height–intelligence correlation: New insights from a bivariate ACE model with assortative mating". Behavior Genetics. 41 (2): 242–252
ACE_model
Statistical data type
status, military ranks, and letter grades for coursework. Ordinal data analysis requires a different set of analyses than other qualitative variables.
Ordinal_data
Curve along which a 3-D surface is at equal elevation
probability density. Isodensanes are used to display bivariate distributions. For example, for a bivariate elliptical distribution the isodensity lines are
Contour_line
Belgian statistician (born 1956)
of scale). With Ida Ruts and John Tukey he introduced the bagplot, a bivariate generalization of the boxplot. His more recent work has focused on concepts
Peter_Rousseeuw
Probability distribution
B C; Ng, N K T (September 2011). "Flexible bivariate beta distributions". Journal of Multivariate Analysis. 102 (8): 1194–1202. doi:10.1016/j.jmva.2011
Distribution of the product of two random variables
Distribution_of_the_product_of_two_random_variables
that the pair ( X , Y ) {\displaystyle (X,Y)} of random variables has a bivariate normal distribution means that every linear combination a X + b Y {\displaystyle
Misconceptions about the normal distribution
Misconceptions_about_the_normal_distribution
Number of values in the final calculation of a statistic that are free to vary
degrees of freedom within each of the populations). Consider an example of bivariate regression: Y i = a + b x i + e i for i = 1 , … , n {\displaystyle
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Numerical computation software system
functions in 1D, including functions with jumps Approximation of smooth bivariate functions (Chebfun2) Approximation of smooth trivariate functions (Chebfun3)
Chebfun
Polynomial whose Laplacian is zero
nontrivial spaces of harmonic polynomials. Consider for instance the bivariate quadratic polynomial p ( x , y ) := a 0 , 0 + a 1 , 0 x + a 0 , 1 y +
Harmonic_polynomial
Predicting and managing water resources
complex. In a bivariate diagram, a linear or higher-order model may be fitted to the data. Factor analysis and principal component analysis are multivariate
Hydrological_model
study other bivariate means and inequalities. Mean Arithmetic mean Geometric mean Stolarsky mean Identric mean Means in Mathematical Analysis E. Neuman
Neuman–Sándor_mean
Middle quantile of a data set or probability distribution
The idea dates back to Wald in 1940 who suggested dividing a set of bivariate data into two halves depending on the value of the independent parameter
Median
Spatial correlation measure
Lee's L is a bivariate spatial correlation coefficient which measures the association between two sets of observations made at the same spatial sites
Lee's_L
Statistical test comparing two probability distributions
Rosenblatt's transformation, and an algorithm is developed to compute it in the bivariate case. An approximate test that can be easily computed in any dimension
Kolmogorov–Smirnov_test
Chinese mathematician and statistician (born 1940)
has helped to develop generalized multivariate analysis, which extends classical multivariate analysis beyond the multivariate normal distribution to
Fang_Kaitai
Statistical field
be defined as a product measure on Cartesian products, characterising bivariate (two-dimensional) or multivariate densities. The geometric structure of
Bayes_space
Images used to represent statistical data visually
the earliest attempts to analyse data. Many familiar forms, including bivariate plots, statistical maps, bar charts, and coordinate paper were used in
Statistical_graphics
Smallest convex set containing a given set
Rousseeuw, Peter J.; Ruts, Ida; Tukey, John W. (1999), "The bagplot: A bivariate boxplot", The American Statistician, 53 (4): 382–387, doi:10.1080/00031305
Convex_hull
models. The Subba Rao–Liporace models, and Subba Rao Gabr window for bivariate spectra are named after him. Subba Rao retired, but was given an emeritus
Tata_Subba_Rao
Statistical algorithm
{\displaystyle Y} . It can be used as a general measure of dependence. In the bivariate case, the ACE algorithm can also be regarded as a method for estimating
Alternating conditional expectations
Alternating_conditional_expectations
Probability distribution
simulating bivariate asymmetric Laplace variables (including for the case of μ = 0 {\displaystyle {\boldsymbol {\mu }}=\mathbf {0} } ). Simulate a bivariate normal
Multivariate Laplace distribution
Multivariate_Laplace_distribution
Every polynomial has a real or complex root
of p(x). In terms of representation, Rp(x)(a, b) and Sp(x)(a, b) are bivariate polynomials in a and b. In the flavor of Gauss's first (incomplete) proof
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Swedish-american Biostatistician
bivariate correlations in resting-state fMRI: A comparison study and a new approach". NeuroImage. "Neuroimaging results altered by varying analysis pipelines"
Martin_A._Lindquist
Number of subsets of a given size
_{n=0}^{\infty }{\binom {n}{k}}y^{n}={\frac {y^{k}}{(1-y)^{k+1}}}.} The bivariate generating function of the binomial coefficients is ∑ n = 0 ∞ ∑ k = 0
Binomial_coefficient
BIVARIATE ANALYSIS
BIVARIATE ANALYSIS
Girl/Female
Hindu
Analysis
Girl/Female
Hindu
Close inspection, A review, Analysis
Girl/Female
Tamil
Sameeksha | ஸமீகà¯à®·à®¾Â
Analysis
Sameeksha | ஸமீகà¯à®·à®¾Â
Girl/Female
Hindu
Analysis
Girl/Female
Tamil
Sameksha | ஸமேகà¯à®·à®¾
Analysis
Sameksha | ஸமேகà¯à®·à®¾
Girl/Female
Muslim
Analysis
Girl/Female
Tamil
Sumiksha | ஸà¯à®®à¯€à®•à¯à®·à®¾Â
Close inspection, A review, Analysis
Sumiksha | ஸà¯à®®à¯€à®•à¯à®·à®¾Â
Girl/Female
Indian, Telugu
Review; Analysis
Girl/Female
Tamil
Samiksha | ஸமீகà¯à®·à®¾
Analysis
Samiksha | ஸமீகà¯à®·à®¾
Girl/Female
Hindu
Analysis
Girl/Female
Indian
Analysis
BIVARIATE ANALYSIS
BIVARIATE ANALYSIS
Boy/Male
Tamil
Destroyer of evil, Killing enemies
Boy/Male
Hindu
Powerful, Warrior
Girl/Female
Sikh
One absorbed in peace and bliss
Girl/Female
Muslim/Islamic
Loving nature
Boy/Male
Tamil
Lord Shiva, Lord Ram
Boy/Male
Tamil
Knowledge
Girl/Female
Indian, Tamil
Tasty
Boy/Male
Australian, British, Czechoslovakian, English, Finnish, German
Princess; Assistant
Boy/Male
Tamil
Belonging to the gods, Divine
Girl/Female
Tamil
BIVARIATE ANALYSIS
BIVARIATE ANALYSIS
BIVARIATE ANALYSIS
BIVARIATE ANALYSIS
BIVARIATE ANALYSIS
a.
Diverging; spreading asunder; widely diverging.
a.
In two rows or series.
a.
Divided in such a manner as to resemble the two lips when the mouth is more or less open; bilabiate.
a.
Alt. of Biseriate
a.
Having two keel-like projections, as the upper palea of grasses.
n.
Delegated office or power; vicarship; the office or oversight of a vicar.
a.
Alt. of Biradiated
a.
Having two rays; as, a biradiate fin.
imp. & p. p.
of Divaricate
a.
Having the throat of a bilabiate corolla nearly closed by a projection of the base of the lower lip; masked, as in the flower of the snapdragon.
v. t. & i.
To alter; to make different; to vary.
a.
Having delegated power, as a vicar; vicarious.
a.
Having two lips, as the corols of certain flowers.
a.
Having the lips widely separated and gaping like an open mouth; as a ringent bilabiate corolla.
v. t.
To divide into two branches; to cause to branch apart.
a.
Forking and diverging; widely diverging; as the branches of a tree, or as lines of sculpture, or color markings on animals, etc.
n.
The separation of a compound substance, by chemical processes, into its constituents, with a view to ascertain either (a) what elements it contains, or (b) how much of each element is present. The former is called qualitative, and the latter quantitative analysis.
v. i.
To diverge; to be divaricate.
p. pr. & vb. n.
of Divaricate
v. i.
To part into two branches; to become bifid; to fork.