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Nonparametric measure of rank correlation
In statistics, Spearman's rank correlation coefficient or Spearman's ρ is a number ranging from -1 to 1 that indicates how strongly two sets of ranks
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Measure of linear correlation
In statistics, the Pearson correlation coefficient (PCC), also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), or simply
Pearson correlation coefficient
Pearson_correlation_coefficient
Statistical relationship
In statistics, correlation is a type of statistical relationship between two random variables or bivariate data. It usually refers to the extent to which
Correlation
Numerical measure of a statistical relationship between variables
{\displaystyle \sum x^{2}} and ∑ y 2 {\displaystyle \sum y^{2}} are the sums of squared x-scores and squared y-scores. Intraclass correlation (ICC) is a descriptive
Correlation_coefficient
Covariance and correlation
cross-correlation of f ( − t ) ¯ {\displaystyle {\overline {f(-t)}}} and g ( t ) {\displaystyle g(t)} ) gives the probability density function of the sum X
Cross-correlation
In chaos theory, the correlation sum is the estimator of the correlation integral, which reflects the mean probability that the states at two different
Correlation_sum
Statistic comparing ordinal rankings
of discordant pairs (see Kendall tau rank correlation coefficient). The sum ∑ a i j 2 {\displaystyle \sum a_{ij}^{2}} is just n ( n − 1 ) / 2 {\displaystyle
Rank_correlation
Concept in probability theory and statistics
In probability theory and statistics, partial correlation measures the degree of association between two random variables, with the effect of a set of
Partial_correlation
Descriptive statistic
In statistics, the intraclass correlation, or the intraclass correlation coefficient (ICC), is a descriptive statistic that can be used when quantitative
Intraclass_correlation
Correlation of a signal with a time-shifted copy of itself, as a function of shift
Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself.
Autocorrelation
Statistic for rank correlation
In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic
Kendall rank correlation coefficient
Kendall_rank_correlation_coefficient
Statistical concept
c {\displaystyle \mathbf {c} ^{\top }\,\mathbf {c} } , the sum of the squared correlations with the dependent variable. If the predictor variables are
Coefficient of multiple correlation
Coefficient_of_multiple_correlation
Statistical measure of association for two binary variables
one of the four sums in the denominator is zero, the denominator can be arbitrarily set to one; this results in a Matthews correlation coefficient of zero
Phi_coefficient
Statistical measure of a dendrogram's faithfulness to the data
statistics, and especially in biostatistics, cophenetic correlation (more precisely, the cophenetic correlation coefficient) is a measure of how faithfully a dendrogram
Cophenetic_correlation
Method of partitioning data points into groups based on their similarity
partitioning data points into groups based on similarity or dissimilarity. Correlation clustering is a clustering framework in which a set of objects is partitioned
Correlation_clustering
In statistics, a measurement of the agreement between two variables
{\displaystyle s_{xy}={\frac {1}{N}}\sum _{n=1}^{N}(x_{n}-{\bar {x}})(y_{n}-{\bar {y}}).} Whereas the ordinary correlation coefficient (Pearson's) is immune
Concordance correlation coefficient
Concordance_correlation_coefficient
total correlation is the amount of information shared among the variables in the set. The sum ∑ i = 1 n H ( X i ) {\displaystyle {\begin{matrix}\sum
Total_correlation
Nonparametric test of the null hypothesis
U} test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test
Mann–Whitney_U_test
Indicator for how well data points fit a line or curve
(which includes an intercept), r2 is simply the square of the sample correlation coefficient (r), between the observed outcomes and the observed predictor
Coefficient_of_determination
The correlation ratio η (eta) is defined as to satisfy η 2 = ∑ x n x ( y ¯ x − y ¯ ) 2 ∑ x , i ( y x i − y ¯ ) 2 {\displaystyle \eta ^{2}={\frac {\sum _{x}n_{x}({\overline
Correlation_ratio
Sequence of data points over time
measures Measures based on the correlation sum Correlation dimension Correlation integral Correlation density Correlation entropy Approximate entropy Sample
Time_series
Linear regression model with a single explanatory variable
to make the sum of these squared deviations as small as possible. In this case, the slope of the fitted line is equal to the correlation between y and
Simple_linear_regression
Correlation coefficient used when one variable is dichotomous
{1}{n-1}}\sum _{i=1}^{n}(X_{i}-{\overline {X}})^{2}}}.} The version of the formula using sn−1 is useful if one is calculating point-biserial correlation coefficients
Point-biserial correlation coefficient
Point-biserial_correlation_coefficient
Measure of dependence
mutual information. While total correlation is bounded by the sum entropies of the n elements, the dual total correlation is bounded by the joint-entropy
Dual_total_correlation
delay. The correlation integral is used to estimate the correlation dimension. An estimator of the correlation integral is the correlation sum: C ( ε )
Correlation_integral
Mapping of data into a single system
Common examples of image similarity measures include cross-correlation, mutual information, sum of squared intensity differences, and ratio image uniformity
Image_registration
Expectation value of time-ordered quantum operators
]}} using its Taylor series, the n-point correlation function becomes a sum of interaction picture correlation functions which can be evaluated using Wick's
Correlation function (quantum field theory)
Correlation_function_(quantum_field_theory)
Statistical measure
In statistics and in probability theory, distance correlation is a measure of dependence between two paired random vectors of arbitrary, not necessarily
Distance_correlation
Measure of the joint variability
not necessarily have the same units. In those situations, we use the correlation coefficient, which normalizes the covariance to a value between -1 and
Covariance
Mathematical image techniques
Digital image correlation and tracking is an optical method that employs tracking and image registration techniques for accurate 2D and 3D measurements
Digital image correlation and tracking
Digital_image_correlation_and_tracking
Statistical measure of how far values spread from their average
absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance
Variance
Statistical measure to determine how suited data is for factor analysis
there are large partial correlations compared to the sum of correlations. In other words, there are widespread correlations which would be a large problem
Kaiser–Meyer–Olkin_test
Statistical method
diagonals of the correlation matrix; FA adjusts the diagonals of the correlation matrix with the unique factors. PCA minimizes the sum of squared perpendicular
Factor_analysis
Method of data analysis
"remarkable" correlations of the correlation matrix, by a solid line (positive correlation) or dotted line (negative correlation). A strong correlation is not
Principal_component_analysis
Statistical measure of the discrepancy between data and an estimation model
− y i ) 2 . {\displaystyle S_{yy}=\sum _{i=1}^{n}({\bar {y}}-y_{i})^{2}.} The Pearson product-moment correlation is given by r = S x y S x x S y y ;
Residual_sum_of_squares
Computational quantum mechanical modelling method to investigate electronic structure
a perturbation theory approach the direct correlation function is given by the sum of the direct correlation in a known system such as hard spheres and
Density_functional_theory
Type of financial derivative
realized correlation formula simplifies to: ρ realized = 2 n ( n − 1 ) ∑ i > j ρ i , j {\displaystyle \rho _{\text{realized }}={\frac {2}{n(n-1)}}\sum _{i>j}{\rho
Correlation_swap
Method of analysing a dynamical system
specific state will recur. It is almost equal with the definition of the correlation sum, where the LOI is excluded from the computation. The next measure is
Recurrence quantification analysis
Recurrence_quantification_analysis
Set of statistical processes for estimating the relationships among variables
least squares computes the unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane)
Regression_analysis
produce three-dimensional data, the Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3-dimensional volumes
Fourier_shell_correlation
Statistic measuring inter-rater agreement for categorical items
{\displaystyle p_{e}=\sum _{k}{\widehat {p_{k,k}}}\ {\overset {\text{ind.}}{=}}\ \sum _{k}{\widehat {p_{k,\cdot }}}\ {\widehat {p_{\cdot ,k}}}=\sum _{k}{\frac {O_{k
Cohen's_kappa
Integral expressing the amount of overlap of one function as it is shifted over another
cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution f ∗ g {\displaystyle f*g} differs from cross-correlation f
Convolution
Procedure for comparing multivariate sample means
the additional sum of squares explained by adding the grouping information and S res {\textstyle S_{\text{res}}} is the residual sum of squares of the
Multivariate analysis of variance
Multivariate_analysis_of_variance
Statistical transformation
z-transformation) of a Pearson correlation coefficient is its inverse hyperbolic tangent (artanh). When the sample correlation coefficient r is near 1 or
Fisher_transformation
Concept in statistical analysis
of the other variable (possibly the independent variable) (see also correlation and simple linear regression). Bivariate analysis can be contrasted with
Bivariate_analysis
Way of inferring information from cross-covariance matrices
are correlations among the variables, then canonical-correlation analysis will find linear combinations of X and Y that have a maximum correlation with
Canonical_correlation
Empirical law on the variance of species in a habitat
to intraclass correlation (ρ) which is defined as ρ = 1 − ∑ x i ( T − x i ) p ( 1 − p ) N T ( T − 1 ) {\displaystyle \rho =1-{\frac {\sum
Taylor's_law
Mathematical model of ferromagnetism in statistical mechanics
total correlation is given by the contribution to the correlation by summing over all paths linking two points, which is bounded above by the sum over
Ising_model
connected correlation function, is a cumulant of a random variable. It can often be obtained by summing over connected Feynman diagrams (the sum over all
Ursell_function
Formal fallacy in statistical interpretation
ecological fallacies are: confusion between ecological correlations and individual correlations, confusion between group average and total average, Simpson's
Ecological_fallacy
Fundamental theorem in probability theory and statistics
{1}{s_{n}^{2+\delta }}}\,\sum _{i=1}^{n}\operatorname {E} \left[\left|X_{i}-\mu _{i}\right|^{2+\delta }\right]=0} is satisfied, then a sum of X i − μ i s n {\textstyle
Central_limit_theorem
Measure of a system's order
mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Description of particle density in statistical mechanics
In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g(r)} in a system of particles (atoms
Radial_distribution_function
Statistical hypothesis test
rank-biserial correlation. If the test statistic T is reported, the rank correlation r is equal to the test statistic T divided by the total rank sum S, or r = T/S
Wilcoxon_signed-rank_test
Data transformation of statistics into rank
include: Friedman test Kruskal–Wallis test Rank products Spearman's rank correlation coefficient Mann–Whitney U test Wilcoxon signed-rank test Van der Waerden
Ranking_(statistics)
Collection of statistical models
formal analysis in a 1918 article on theoretical population genetics, The Correlation Between Relatives on the Supposition of Mendelian Inheritance. His first
Analysis_of_variance
Statistical modeling method
to use an all positive correlations (APC) arrangement of the strongly correlated variables under which pairwise correlations among these variables are
Linear_regression
Simultaneous observation and analysis of more than one outcome variable
over time. Iconography of correlations consists in replacing a correlation matrix by a diagram where the "remarkable" correlations are represented by a solid
Multivariate_statistics
Measure of variation in statistics
\left({\frac {1}{N}}\sum _{i=1}^{N}X_{i}\right)={\frac {1}{N^{2}}}\operatorname {var} \left(\sum _{i=1}^{N}X_{i}\right)\\&={\frac {1}{N^{2}}}\sum _{i=1}^{N}\operatorname
Standard_deviation
due to the way in which variances behave when summing correlated random variables. To sell correlation, investors can: Sell a call option on the index
Correlation_trading
Statistical measure of the magnitude of a phenomenon
deviations within each groups. SS is the sum of squares in ANOVA. Another measure that is used with correlation differences is Cohen's q. This is the difference
Effect_size
Statistical hypothesis test
t_{\text{score}}={\frac {r{\sqrt {n-2}}}{\sqrt {1-r^{2}}}},} where r is the Pearson correlation coefficient. The tscore, intercept can be determined from the tscore
Student's_t-test
{\frac {\sum _{i}(x_{i}-{\bar {x}})^{2}}{n}}}=s_{x}{\sqrt {\frac {n-1}{n}}}} . When the theoretical assumptions are satisfied, the biserial correlation coefficient
Biserial_correlation
Study of collection and analysis of data
Chi-squared test Correlation Factor analysis Mann–Whitney U Mean square weighted deviation (MSWD) Pearson product-moment correlation coefficient Regression
Statistics
Number taken as representative of a list of numbers
average is the arithmetic mean, also known as "arithmetic average" i.e. the sum divided by the count, so the "average" of the list of numbers [2, 3, 4, 7
Average
Quantum-mechanical framework for simulating molecules and solids
_{n\rightarrow \infty }\sum _{j=2}^{n}E_{c}^{\text{GLn}}[n]=\sum _{j=2}^{\infty }E_{j}=E_{c}[n]} and the corresponding correlation potential v c ( r ) =
Görling–Levy perturbation theory
Görling–Levy_perturbation_theory
In statistics, scaled correlation is a form of a coefficient of correlation applicable to data that have a temporal component such as time series. It
Scaled_correlation
Representation learning technique
Similarity Correlation Euclidean Distance Distance between ends of vectors | a − b | {\displaystyle |a-b|} ∑ ( a n − b n ) 2 {\displaystyle {\sqrt {\sum
Embedding_(machine_learning)
Type of statistical measure over subsets of a dataset
{\text{next}}}&={\frac {1}{k}}\sum _{i=n-k+2}^{n+1}p_{i}\\&={\frac {1}{k}}{\Big (}\underbrace {p_{n-k+2}+p_{n-k+3}+\dots +p_{n}+p_{n+1}} _{\sum _{i=n-k+2}^{n+1}p_{i}}+\underbrace
Moving_average
Table that displays the frequency of variables
the Theory of Contingency and Its Relation to Association and Normal Correlation", part of the Drapers' Company Research Memoirs Biometric Series I published
Contingency_table
Statistical hypothesis test
1 k p i = n {\displaystyle {\begin{aligned}&\sum _{i=1}^{k}{p_{i}}=1\\[8pt]&\sum _{i=1}^{k}{m_{i}}=n\sum _{i=1}^{k}{p_{i}}=n\end{aligned}}} Pearson proposed
Chi-squared_test
Mathematical conjecture
mathematics, Montgomery's pair correlation conjecture is a conjecture made by Hugh Montgomery (1973) that the pair correlation between pairs of zeros of the
Montgomery's pair correlation conjecture
Montgomery's_pair_correlation_conjecture
Statistical phenomenon
{y}}-{\hat {\beta }}\,{\bar {x}},\end{aligned}}} where rxy is the sample correlation coefficient between x and y, sx is the standard deviation of x, and sy
Regression_toward_the_mean
Method of estimating the parameters of a statistical model, given observations
}}^{2}={\frac {1}{n}}\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}={\frac {1}{n}}\sum _{i=1}^{n}x_{i}^{2}-{\frac {1}{n^{2}}}\sum _{i=1}^{n}\sum _{j=1}^{n}x_{i}x_{j}
Maximum_likelihood_estimation
Statistical term
path tracing rules, for calculating the correlation between two variables. The correlation is equal to the sum of the contribution of all the pathways
Path_analysis_(statistics)
Approximation method in statistics
least squares is a method to determine the best-fit model by minimizing the sum of the squared residuals—the differences between observed values and the
Least_squares
Test statistic
− e t − 1 ) 2 ∑ t = 1 T e t 2 , {\displaystyle d={\sum _{t=2}^{T}(e_{t}-e_{t-1})^{2} \over {\sum _{t=1}^{T}e_{t}^{2}}},} where T {\textstyle T} is the
Durbin–Watson_statistic
Statistical measure used in survey research
total of n = ∑ n k {\displaystyle n=\sum n_{k}} observations. The observations have a block diagonal correlation matrix in which every pair of observations
Design_effect
Statistical test comparing two probability distributions
{\begin{aligned}\operatorname {Pr} (K\leq x)&=1-2\sum _{k=1}^{\infty }(-1)^{k-1}e^{-2k^{2}x^{2}}\\&={\frac {\sqrt {2\pi }}{x}}\sum _{k=1}^{\infty }e^{-(2k-1)^{2}\pi ^{2}/(8x^{2})}
Kolmogorov–Smirnov_test
Grouping a set of objects by similarity
subspace clustering and DiSH) and correlation clustering (HiCO, hierarchical correlation clustering, 4C using "correlation connectivity" and ERiC exploring
Cluster_analysis
Effect of variables' uncertainties on the uncertainty of a function based on them
uncertainties are correlated then covariance must be taken into account. Correlation can arise from two different sources. First, the measurement errors may
Propagation_of_uncertainty
Statistics concept
{\begin{bmatrix}\sum _{i=1}^{n}x_{i}^{0}&\sum _{i=1}^{n}x_{i}^{1}&\sum _{i=1}^{n}x_{i}^{2}&\cdots &\sum _{i=1}^{n}x_{i}^{m}\\\sum _{i=1}^{n}x_{i}^{1}&\sum _{i=1}^{n}x_{i}^{2}&\sum
Polynomial_regression
Variable representing a random phenomenon
variables, sometimes to construct them, and to define notions such as correlation and dependence or independence based on a joint distribution of two or
Random_variable
Statistical measure of association
of their maximum possible variation. φc2 is the mean square canonical correlation between the variables.[citation needed] In the case of a 2 × 2 contingency
Cramér's_V
Method used in statistics, pattern recognition, and other fields
Structure Correlation Coefficients: The correlation between each predictor and the discriminant score of each function. This is a zero-order correlation (i.e
Linear_discriminant_analysis
Measure of covariance of components of a random vector
related to the covariance matrix is the matrix of Pearson product-moment correlation coefficients between each of the random variables in the random vector
Covariance_matrix
Statistical model for a binary dependent variable
) ln ( 1 − p k ) ) {\displaystyle \ell =\sum _{k:y_{k}=1}\ln(p_{k})+\sum _{k:y_{k}=0}\ln(1-p_{k})=\sum _{k=1}^{K}\left(\,y_{k}\ln(p_{k})+(1-y_{k})
Logistic_regression
Statistics concept
guaranteed to be positive semi-definite. This could lead to estimated correlations having absolute values which are greater than one, and/or a non-invertible
Estimation of covariance matrices
Estimation_of_covariance_matrices
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
Square Deviation (RMSD). While many natural processes indeed show a correlation between the average value and the amount of variation around it, accurate
Coefficient_of_variation
Theory and technique of psychological measurement
relating to measurement theory (e.g., item response theory, intraclass correlation) or specialize as learning and development professionals. The word psychometry
Psychometrics
Probabilistic problem-solving algorithm
method for modified geometry of Macpherson suspension based on Pearson Correlation Coefficient". Vehicle System Dynamics. 55 (6): 827–852. Bibcode:2017VSD
Monte_Carlo_method
Measure of dependence between two variables
limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint
Mutual_information
Comparison of two distributions
"probability plot correlation coefficient" (PPCC plot) is the correlation coefficient between the paired sample quantiles. The closer the correlation coefficient
Q–Q_plot
Quantum version of the classical action
spacelike separations. General correlation functions can always be written as a sum of products of connected correlation functions. The quantum effective
Effective_action
processing) Topological data analysis Tornqvist index Total correlation Total least squares Total sum of squares Total survey error Total variation distance –
List_of_statistics_articles
Middle quantile of a data set or probability distribution
) k f ( v ) N − i − k {\displaystyle \Pr(\operatorname {med} =v)=\sum _{i=0}^{n}\sum _{k=0}^{n}{\frac {N!}{i!(N-i-k)!k!}}F(v-1)^{i}(1-F(v))^{k}f(v)^{N-i-k}}
Median
Statistical method for handling multiple comparisons
(including the case of negative correlation), c(m) is the harmonic number: c ( m ) = ∑ i = 1 m 1 i {\displaystyle c(m)=\sum _{i=1}^{m}{\frac {1}{i}}} . Note
False_discovery_rate
Concept in quantum optics
In quantum optics, correlation functions are used to characterize the statistical and coherence properties – the ability of waves to interfere – of electromagnetic
Higher_order_coherence
Bias in causal inference
cannot be fully described by correlations or associations alone. The presence of confounders helps explain why correlation does not imply causation, and
Confounding
Theorem about independent random variables
In statistics, Lukacs's proportion-sum independence theorem is a result that is used when studying proportions, in particular the Dirichlet distribution
Lukacs's proportion-sum independence theorem
Lukacs's_proportion-sum_independence_theorem
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