Free reference · 596 entries
The words, before the course.
Short, plain definitions of the terms that turn up in statistics and data science — what they mean, and how they relate to each other. Nothing to sign in for.
596 entries
A
- A Priori ProbabilityA priori probability is the probability estimate prior to receiving new information. See also Bayes Theorem and posterior probability.
- A-B TestAn A-B test is a classic statistical design in which individuals or subjects are randomly split into two groups and some intervention or treatment is applied – one group gets treatment A, the other treatment B.
- Acceptance RegionIn hypothesis testing, the test procedure partitions all the possible sample outcomes into two subsets (on the basis of whether the observed value of the test statistic is smaller than a threshold value or…
- Acceptance SamplingAcceptance sampling is the use of sampling methods to determine whether a shipment of products or components is of sufficient quality to be accepted.
- Acceptance Sampling PlansFor a shipment or production lot, an acceptance sampling plan defines a sampling procedure and gives decision rules for accepting or rejecting the shipment or lot, based on the sampling results.
- Additive effectAn additive effect refers to the role of a variable in an estimated model. A variable that has an additive effect can merely be added to the other terms in a model to determine its effect on the independent…
- Additive ErrorAdditive error is the error that is added to the true value and does not depend on the true value itself.
- Agglomerative Methods (of Cluster Analysis)In agglomerative methods of hierarchical cluster analysis, the clusters obtained at the previous step are fused into larger clusters.
- Aggregate MeanIn ANOVA and some other techniques used for analysis of several samples, the aggregate mean is the mean for all values in all samples combined, as opposed to the mean values of the individual samples.
- Alpha LevelSee Type I Error.
- Alpha Spending FunctionIn the interim monitoring of clinical trials, multiple looks are taken at the accruing results.
- Alternate-Form ReliabilityThe alternate-form reliability of a survey instrument, like a psychological test, helps to overcome the “practice effect”, which is typical of the test-retest reliability.
- Alternative HypothesisIn hypothesis testing, there are two competing hypotheses – the null hypothesis and the alternative hypothesis.
- Analysis of CommonalityAnalysis of commonality is a method for causal modeling. In a simple case of two independent variables x1 and x2, for example, analysis of commonality posits three sources of causation, described by three…
- Analysis of Variance (ANOVA)A statistical technique which helps in making inference whether three or more samples might come from populations having the same mean; specifically, whether the differences among the samples might be…
- ANOVASee Analysis of variance
- ARIMAARIMA as an acronym for Autoregressive Integrated Moving Average Model (also known as Box-Jenkins model).
- Arithmetic MeanThe arithmetic mean is a synonym of the mean. The word “arithmetic” is used to discern this statistic from other statistics having “mean” in their names, like the geometric mean, the harmonic mean, the…
- Association RulesAssociation rules is a method of data mining. The idea is to find a statistical association between some items in a large set of items, e.g.
- Asymptotic EfficiencyFor an unbiased estimator, asymptotic efficiency is the limit of its efficiency as the sample size tends to infinity.
- Asymptotic PropertyAn asymptotic property is a property of an estimator that holds as the sample size approaches infinity.
- Asymptotic Relative Efficiency (of estimators)Unbiased estimators are usually compared in terms of their variances. The limit (as the sample size tends to infinity) of the ratio of the variance of the first estimator to the variance of the second…
- Asymptotically Unbiased EstimatorAn asymptotically unbiased estimator is an estimator that is unbiased as the sample size tends to infinity.
- AttributeIn data analysis or data mining, an attribute is a characteristic or feature that is measured for each observation (record) and can vary from one observation to another.
- AutocorrelationSee Serial correlation.
- AutoregressionAutoregression refers to a special branch of regression analysis aimed at analysis of time series.
- Autoregression and Moving Average (ARMA) ModelsThe autoregression and moving average (ARMA) models are used in time series analysis to describe stationary time series.
- Autoregressive (AR) ModelsThe autoregressive (AR) models are used in time series analysis. to describe stationary time series.
- Average DeviationThe average deviation or the average absolute deviation is a measure of dispersion. It is the average of absolute deviations of the individual values from the median or from the mean.
- Average Group LinkageThe average group linkage is a method of calculating distance between clusters in hierarchical cluster analysis.
- Average Linkage ClusteringThe average linkage clustering is a method of calculating distance between clusters in hierarchical cluster analysis.
- Azure MLAzure is the Microsoft Cloud Computing Platform and Services. ML stands for Machine Learning, and is one of the services.
B
- Backward EliminationBackward elimination is one of several computer-based iterative variable-selection procedures.
- Bag-of-wordsBag-of-words is a simplified natural language processing concept. Text documents are parsed and output as collections of words (i.e.
- BaggingIn predictive modeling, bagging is an ensemble method that uses bootstrap replicates of the original training data to fit predictive models.
- BanditsBandits refers to a class of algorithms in which users or subjects make repeated choices among, or decisions in reaction to, multiple alternatives.
- Bayes’ TheoremBayes theorem is a formula for revising a priori probabilities after receiving new information.
- Bernoulli DistributionA random variable x has a Bernoulli distribution with parameter 0 < p < 1 if 1–p, x=0 p, x=1 0, x à{0, 1} where P(A) is the probability of outcome A.
- Bernoulli Distribution (Graphical)A random variable x has a Bernoulli distribution with parameter 0 < p < 1 if where P(A) is the probability of outcome A.
- Beta Distribution (Graphical)Suppose x1, x2, … , xn are n independent values of a random variable uniformly distributed within the interval [0,1].
- BiasA general statistical term meaning a systematic (not random) deviation of an estimate from the true value.
- Biased EstimatorAn estimator is a biased estimator if its expected value is not equal to the value of the population parameter being estimated.
- BimodalBimodal literally means “two modes” and is typically used to describe distributions of values that have two centers.
- Binomial DistributionUsed to describe an experiment, event, or process for which the probability of success is the same for each trial and each trial has only two possible outcomes.
- Bonferroni AdjustmentBonferroni adjustment is used in multiple comparison procedures to calculate an adjusted probability a of comparison-wise type I error from the desired probability aFW0 of family-wise type I error.
- Bonferroni Adjustment (Graphical)Bonferroni adjustment is used in multiple comparison procedures to calculate an adjusted probability of comparison-wise type I error from the desired probability of family-wise type I error.
- BoostingIn predictive modeling, boosting is an iterative ensemble method that starts out by applying a classification algorithm and generating classifications.
- BootstrappingBootstrapping is sampling with replacement from observed data to estimate the variability in a statistic of interest.
- Box PlotA box plot is a graph that characterizes the pattern of variation of the data. The plot simultaneously displays several measures of central tendency and dispersion of the data at hand.
- Box’s MBox’s M is a statistic which tests the homoscedasticity assumption in MANOVA – that is the assumption that all covariances are the same for any category.
C
- Calibration SampleThe calibration sample is the subset of the data available to a data mining routine used as the training set.
- Categorical DataCategorical data are reflecting the classification of objects into different categories. For example, people who receive a mail order offer might be classified as “no response,” “purchase and pay,”…
- Categorical Data AnalysisCategorical data analysis is a branch of statistics dealing with categorical data. This sort of analysis is of great practical importance because a wide variety of data are of a categorical nature.
- Causal modelingCausal modeling is aimed at advancing reasonable hypotheses about underlying causal relationships between the dependent and independent variables.
- Census SurveyIn a census survey , all units from the population of interest are analyzed. A related concept is the sample survey, in which only a subset of the population is taken.
- Central Limit TheoremThe central limit theorem states that the sampling distribution of the mean approaches Normality as the sample size increases, regardless of the probability distribution of the population from which the…
- Central LocationCentral location is a synonym of central tendency.
- Central Tendency (Measures)Any measure of central tendency provides a typical value of a set of values . Normally, it is a value around which values are grouped.
- CentroidThe centroid of several continuous variables is the vector of means of those variables. The concept of centroid plays the same role, for example, in multiple analysis of variance (MANOVA) as the mean plays…
- CHAIDCHAID stands for Chi-squared Automatic Interaction Detector. It is a method for building classification trees and regression trees from a learning sample comprising already-classified objects.
- Chebyshev’s TheoremFor any positive constant ’k’, the probability that a random variable will take on a value within k standard deviations of the mean is at least 1 – 1/k2.
- Chernoff FacesChernoff faces are a category of icon plots. Each unit is represented as a schematic face.
- Chi-Square DistributionThe square of a random variable having standard normal distribution is distributed as chi-square with 1 degree of freedom.
- Chi-Square StatisticThe chi-square statistic (or -statistic) measures agreement between the observed and hypothetical frequencies.
- Chi-Square TestChi-square test (or -test) is a statistical test for testing the null hypothesis that the distribution of a discrete random variable coincides with a given distribution.
- Circular Icon PlotsCircular icon plots are a category of icon plots. Each variable is represented by a ray or direction; all rays start in the center.
- Classification and Regression Trees (CART)Classification and regression trees (CART) are a set of techniques for classification and prediction.
- Classification TreesClassification trees are one of the CART techniques. The main distinction from regression trees (another CART technique) is that the dependent variable is categorical.
- Cluster AnalysisIn multivariate analysis, cluster analysis refers to methods used to divide up objects into similar groups, or, more precisely, groups whose members are all close to one another on various dimensions being…
- Clustered SamplingClustered sampling is a sampling technique based on dividing the whole population into groups (“clusters”), then using random sampling to select elements from the groups.
- Cochran-Mantel-Haenszel (CMH) testThe Cochran-Mantel-Haenszel (CMH) test compares two groups on a binary response, adjusting for control variables.
- Cochran’s Q StatisticCochran’s Q statistic is computed from replicated measurements data with binary responses.
- Coefficient of DeterminationSST r2 = SSR , where SSR is the sum of squares due to regression, SST is the total sum of squares.
- Coefficient of variationThe coefficient of variation is the standard deviation of a data set, divided by the mean of the same data set.
- Cohen’s KappaCohen’s kappa is a measure of agreement for Categorical data. It is a special case of the Kappa statistic corresponding to the case of only 2 raters.
- Cohort dataCohort data records multiple observations over time for a set of individuals or units tied together by some event (say, born in the same year).
- Cohort studyA cohort study is a longitudinal study that identifies a group of subjects sharing some attributes (a “cohort”) then takes measurements on the subjects at various points in time and records data for the group.
- CointegrationCointegration is a statistical tool for describing the co-movement of data measured over time.
- Collaborative filteringCollaborative filtering algorithms are used to predict whether a given individual might like, or purchase, an item.
- CollinearityIn regression analysis, collinearity of two variables means that strong correlation exists between them, making it difficult or impossible to estimate their individual regression coefficients reliably.
- Column icon plotsSee sequential icon plots.
- Comparison-wise Type I ErrorIn multiple comparison procedures, the comparison-wise type I error is the probability that, even if the samples come from the same population, you will wrongly conclude that they differ.
- Complete Block DesignIn complete block design, every treatment is allocated to every block. In other words, every combination of treatments and conditions (blocks) is tested.
- Complete Linkage ClusteringThe complete linkage clustering (or the farthest neighbor method) is a method of calculating distance between clusters in hierarchical cluster analysis.
- Complete StatisticA sufficient statistic T is called a complete statistic if no function of it has zero expected value for all distributions concerned unless this function itself is zero for all possible distributions…
- Composite HypothesisA statistical hypothesis which does not completely specify the distribution of a random variable is referred to as a composite hypothesis.
- Concurrent ValidityThe concurrent validity of survey instruments, like the tests used in psychometrics, is a measure of agreement between the results obtained by the given survey instrument and the results obtained for the…
- Conditional ProbabilityWhen probabilities are quoted without specification of the sample space, it could result in ambiguity when the sample space is not self-evident.
- Confidence IntervalA confidence interval is an interval that brackets a sample estimate that quantifies uncertainty around this estimate.
- Consistent EstimatorAn estimator is a measure or metric intended to be calculated from a sample drawn from a larger population.
- Construct ValidityIn psychometrics, the construct validity of a survey instrument or psychometric test measures how well the instrument performs in practice from the standpoint of the specialists who use it.
- Content ValidityThe content validity of survey instruments, like psychological tests, is assessed by overview of the items by trained individuals and/or by the individuals from the target population.
- Contingency TableA contingency table is a tabular representation of categorical data. A contingency table usually shows frequencies for particular combinations of values of two discrete random variables X and Y.
- Contingency Tables AnalysisContingency tables analysis is a central branch of categorical data analysis, and is focused on the analysis of data represented as contingency tables.
- Continuous DistributionA continuous distribution describes probabilistic properties of a random variable which takes on a continuous (not countable) set of values – a continuous random variable.
- Continuous Random VariableA continuous random variable is any random variable which takes on values on a continuous scale.
- Continuous Sample SpaceIf a sample space contains an infinite number of sample points constituting a continuum, then such a sample space is said to be a continuous sample space.
- Continuous vs. Discrete DistributionsA discrete distribution is one in which the data can only take on certain values, for example integers.
- Control ChartsControl charts are used to track regular measurements of an ongoing process, and to signal when such a process had reached the point of going “out of control” (i.e.
- Convergent ValidityIn psychometrics, the convergent validity of a survey instrument or psychometric test indicates the degree of agreement between measurements of the same trait obtained by different approaches supposed to…
- Convolution of Distribution FunctionsIf F1(·) and F1(·) are distribution functions, then the function F(·) F(x) = ó õ F1(x–y) dF2(y) is called the convolution of distribution functions F1 and F2.
- Convolution of Distribution Functions (Graphical)If F1(·) and F1(·) are distribution functions, then the function F(·) is called the convolution of distribution functions F1 and F2.
- Correlation CoefficientThe correlation coefficient indicates the degree of linear relationship between two variables.
- Correlation MatrixA Correlation matrix describes correlation among M variables. It is a square symmetrical MxM matrix with the (ij)th element equal to the correlation coefficient r_ij between the (i)th and the (j)th variable.
- Correlation StatisticThe correlation statistic is one of the statistics used in the generalized Cochran-Mantel-Haenszel tests.
- Correspondence analysisCorrespondence analysis (CA) is an approach to representing categorical data in an Euclidean space, suitable for visual analysis.
- Correspondence PlotA correspondence plot represents the results of correspondence analysis (CA). For each category (possible value of a variable), its scores derived by CA for the first two dimensions are depicted as a point…
- Countable Sample SpaceIf a sample space contains finite or countably infinite number of sample points then such a sample space is referred to as a countable sample space.
- CovarianceThe covariance between two random variables X and Y is the expected value of the product of the variables’ deviations from their means.
- CovariateIn design of experiments, a covariate is an independent variable not manipulated by the experimenter but still affecting the response.
- Cover timeCover time is the expected number of steps in a random walk required to visit all the vertices of a connected graph (a graph in which there is always a path, consisting of one or more edges, between any two…
- Cox-RegressionSee Proportional hazard model
- Cramer – Rao InequalityEvery unbiased estimator has a variance greater than or equal to a lower bound called the Cramer – Rao lower bound.
- Criterion ValidityThe criterion validity of survey instruments, like the tests used in psychometrics, is a measure of agreement between the results obtained by the given survey instrument and more “objective” results for the…
- Critical RegionSee Acceptance region
- Cross sectional studyCross sectional studies are those that record data from a sample of subjects at a given point in time.
- Cross-sectional AnalysisCross-sectional analysis is concerned with statistical inference from cross-sectional data.
- Cross-sectional DataCross-sectional data refer to observations of many different individuals (subjects, objects) at a given time, each observation belonging to a different individual.
- Cross-tabulation TablesA cross-tabulation table represents the joint frequency distribution of two discrete variables.
- Cross-ValidationCross-validation is a general computer-intensive approach used in estimating the accuracy of statistical models.
- Crossover DesignIn randomized trials, a crossover design is one in which each subject receives each treatment, in succession.
- Cumulative Frequency DistributionA cumulative frequency distribution is a summary of a set of data showing the frequency (or number) of items less than or equal to the upper class limit of each class.
- Cumulative Relative Frequency DistributionA cumulative relative frequency distribution is a tabular summary of a set of data showing the relative frequency of items less than or equal to the upper class class limit of each class.
- Curb-stoningIn survey research, curb-stoning refers to the deliberate fabrication of survey interview data by the interviewer.
- Curse of DimensionalityThe curse of dimensionality is the affliction caused by adding variables to multivariate data models.
D
- DataData are recorded observations made on people, objects, or other things that can be counted, measured, or quantified in some way.
- Data MiningData mining is concerned with finding latent patterns in large data bases. The goal is to discover unsuspected relationships that are of practical importance, e.g., in business.
- Data PartitionData partitioning in data mining is the division of the whole data available into two or three non-overlapping sets: the training set, the validation set, and the test set.
- Data ProductA data product is a product or service whose value is derived from using algorithmic methods on data, and which in turn produces data to be used in the same product, or tangential data products.
- DecileDeciles are percentiles taken in tens. The first decile is the 10th percentile, the second decile is the 20th percentile, etc.
- Decile LiftIn predictive modeling, the goal is to make predictions about outcomes on a case-by-case basis: an insurance claim will be fraudulent or not, a tax return will be correct or in error, a subscriber will…
- Decision TreesIn the machine learning community, a decision tree is a branching set of rules used to classify a record, or predict a continuous value for a record.
- Deep LearningDeep Learning refers to complex multi-layer neural nets. They are especially suitable for image and voice recognition, and for unsupervised tasks with complex, unstructured data.
- Degrees of FreedomFor a set of data points in a given situation (e.g. with mean or other parameter specified, or not), degrees of freedom is the minimal number of values which should be specified to determine all the data…
- DendrogramThe dendrogram is a graphical representation of the results of hierarchical cluster analysis.
- Density (of Probability)A probability density function or curve is a non-negative function ( ) that describes the distribution of a continuous random variable.
- Dependent and Independent VariablesStatistical models normally specify how one set of variables, called dependent variables, functionally depend on another set of variables, called independent variables.
- Dependent EventsSee Independent Events.
- Descriptive StatisticsDescriptive statistics refers to statistical techniques used to summarize and describe a data set, and also to the statistics (measures) used in such summaries.
- Design of ExperimentsDesign of experiments is concerned with optimization of the plan of experimental studies. The goal is to improve the quality of the decision that is made from the outcome of the study on the basis of…
- Detrended Correspondence AnalysisDetrended correspondence analysis is an extension of correspondence analysis (CA) aimed at addressing a deficiency of correspondence analysis.
- DichotomousDichotomous (outcome or variable) means “having only two possible values”, e.g. “yes/no”, “male/female”, “head/tail”, “age > 35 / age <= 35” etc.
- Differencing (of Time Series)Differencing of a time series in discrete time is the transformation of the series to a new time series where the values are the differences between consecutive values of .
- Directed vs. Undirected NetworkIn a directed network, connections between nodes are directional. For example, in a Twitter network, Smith might follow Jones but that does not mean that Jones follows Smith.
- Discrete DistributionA discrete distribution describes the probabilistic properties of a random variable that takes on a set of values that are discrete, i.e.
- Discrete Random VariableA random variable whose range of possible values is finite or countably infinite is said to be a discrete random variable.
- Discriminant AnalysisDiscriminant analysis is a method of distinguishing between classes of objects. The objects are typically represented as rows in a matrix.
- Dispersion (Measures of)Measures of dispersion express quantitatively the degree of variation or dispersion of values in a population or in a sample.
- Disproportionate Stratified Random SamplingSee Stratified Sampling (method ii).
- Dissimilarity MatrixThe dissimilarity matrix (also called distance matrix) describes pairwise distinction between M objects.
- DistanceDendrogram: Statistical distance is a measure calculated between two records that are typically part of a larger dataset, where rows are records and columns are variables.
- Distance MatrixDistance matrix is often used as a synonym for dissimilarity matrix. The “distance” does not necessarily means distance in space.
- Divergent ValidityIn psychometrics, the divergent validity of a survey instrument, like an IQ-test, indicates that the results obtained by this instrument do not correlate too strongly with measurements of a similar but…
- Divisive Methods (of Cluster Analysis)In divisive methods of hierarchical cluster analysis, the clusters obtained at the previous step are subdivided into smaller clusters.
- Dunn TestThe Dunn test is a method for multiple comparisons, which generalizes the Bonferroni adjustment procedure.
E
- EconometricsEconometrics is a discipline concerned with the application of statistics and mathematics to various problems in economics and economic theory.
- EdgeAn edge is a link between two people or entities in a network. Edges can be directed or undirected.
- EffectIn design of experiments, the effect of a factor is an additive term of the model, reflecting the contribution of the factor to the response.
- Effect SizeIn a study or experiment with two groups (usually control and treatment), the investigator typically has in mind the magnitude of the difference between the two groups that he or she wants to be able to…
- EfficiencyFor an unbiased estimator, efficiency indicates how much its precision is lower than the theoretical limit of precision provided by the Cramer-Rao inequality.
- Endogenous VariableEndogenous variables in causal modeling are the variables with causal links (arrows) leading to them from other variables in the model.
- Ensemble MethodsIn predictive modeling, ensemble methods refer to the practice of taking multiple models and averaging their predictions.
- Erlang DistributionThe Erlang distribution with parameters (n, m) characterizes the distribution of time intervals until the emergence of n events in a Poisson process with parameter m .
- ErrorError is a general concept related to deviation of the estimated quantity from its true value: the greater the deviation, the greater the error.
- Error Spending FunctionSee alpha spending function.
- EstimationEstimation is deriving a guess about the actual value of a population parameter (or parameters) from a sample drawn from this population.
- EstimatorA statistic, measure, or model, applied to a sample, intended to estimate some parameter of the population that the sample came from.
- EventIn probability theory, an event is an outcome or defined collection of outcomes of a random experiment.
- Exact TestsExact tests are hypothesis tests that are guaranteed to produce Type-I error at or below the nominal alpha level of the test when conducted on samples drawn from a null model.
- Exogenous VariableExogenous variables in causal modeling are the variables with no causal links (arrows) leading to them from other variables in the model.
- Expected ValueThe expected value of a random variable is nothing but the arithmetic mean. For a discrete random variable, the expected value is the weighted average of the possible values of the random variable, the…
- ExperimentAny process of observation or measurement is called an experiment in statistics. For example, counting the number people visiting a restaurant in a day is an experiment, and so is checking the number…
- Explanatory VariableExplanatory variable is a synonym for independent variable.
- Exponential DistributionThe exponential distribution is a one-sided distribution completely specified by one parameter r > 0; the density of this distribution is re–rx, x ³ 0 0, x < 0 The mean of the exponential distribution is…
- Exponential Distribution (Graphical)The exponential distribution is a one-sided distribution completely specified by one parameter ; the density of this distribution is The mean of the exponential distribution is .
- Exponential FilterThe exponential filter is the simplest linear recursive filter. Exponential filters are widely used in time series analysis, especially for forecasting time series (see the short course Time Series…
F
- F DistributionThe F distribution is a family of distributions differentiated by two parameters: m1 (degrees of freedom, numerator) and m2 (degrees of freedom, denominator).
- F Distribution (Graphical)The F distribution is a family of distributions differentiated by two parameters: m1 (degrees of freedom, numerator) and m2 (degrees of freedom, denominator).
- Face ValidityThe face validity of survey instruments and tests used in psychometrics, is assessed by cursory review of the items (questions) by untrained individuals.
- FactorIn design of experiments, factor is an independent variable manipulated by the experimenter.
- Factor AnalysisExploratory research on a topic may identify many variables of possible interest, so many that their sheer number can become a hindrance to effective and efficient analysis.
- Fair GameA game of chance is said to be fair if each player’s expected payoff is zero. A game in which I roll a die and receive 12 for a 1 or 2 and lose 6 otherwise (3-6) is a fair game.
- Family-wise Type I ErrorIn multiple comparison procedures, family-wise type I error is the probability that, even if all samples come from the same population, you will wrongly conclude that at least one pair of populations differ.
- Family-wise Type I Error (Graphical)In multiple comparison procedures, family-wise type I error is the probability that, even if all samples come from the same population, you will wrongly conclude that at least one pair of populations differ.
- Farthest Neighbor ClusteringThe farthest neighbor clustering is a synonym for complete linkage clustering.
- FeatureThis term is used synonymously with attribute and variable, it is actually an independent variable (see dependent and independent variables).
- Feature engineeringIn predictive modeling, a key step is to turn available data (which may come from varied sources and be messy) into an orderly matrix of rows (records to be predicted) and columns (predictor variables or…
- Feature SelectionIn predictive modeling, feature selection, also called variable selection, is the process (usually automated) of sorting through variables to retain variables that are likely to be informative in…
- Features vs. VariablesThe predictors in a predictive model are sometimes given different terms by different disciplines.
- FilterA filter is an algorithm for processing a time series or random process. There are two major classes of problems solved by filters: 1.
- Finite Sample SpaceIf a sample space contains a finite number of elements, then the sample space is said to be a finite sample space.
- Fisher’s Exact TestFisher’s exact test is the first (historically) permutation test. It is used with two samples of binary data, and tests the null hypothesis that the two samples are drawn from populations with equal but…
- Fixed Effects (Graphical)The term “fixed effects” (as contrasted with “random effects”) is related to how particular coefficients in a model are treated – as fixed or random values.
- Fleming ProcedureFleming procedure (or O’Brien-Fleming multiple testing procedure) is a simple multiple testing procedure for comparing two treatments when the response to treatment is dichotomous.
- Forward SelectionForward selection is one of several computer-based iterative variable-selection procedures.
- Fourier SpectrumAny continuous function defined on a finite interval of length can be represented as a weighted sum of cosine functions with periods : where is the frequency of the i-th Fourier component; is the amplitude…
- Frequency DistributionA frequency distribution is a tabular summary of a set of data showing the frequency (or number) of items in each of several non-overlapping classes (or bins).
- Frequency Interpretation of ProbabilityThe frequency interpretation of probability is the most widely held of several ways of interpreting the meaning of the concept of “probability”.
- Functional Data Analysis (FDA)In functional data analysis (FDA), data are considered as continuous functions (or curves).
G
- Gamma DistributionA random variable x is said to have a gamma-distribution with parameters a > 0 and l > 0 if its probability density p(x) is G(a) la xa–1 e–lx, x > 0; 0,
- Gamma Distribution (Graphical)A random variable x is said to have a gamma-distribution with parameters a > 0 and l > 0 if its probability density p(x) is G(a) la xa–1 e–lx, x > 0; 0,
- Gaussian DistributionSee Normal Distribution.
- Gaussian FilterThe Gaussian filter is a linear filter that is usually used as a smoother. The output of the gaussian filter at the moment is the weighted mean of the input values, and the weights are defined by formula…
- General Association StatisticThe general association statistic is one of the statistics used in the generalized Cochran-Mantel-Haenszel tests.
- General Linear ModelGeneral (or generalized) linear models (GLM), in contrast to linear models, allow you to describe both additive and non-additive relationship between a dependent variable and N independent variables.
- General Linear Model for a Latin SquareIn design of experiment, a Latin square is a three-factor experiment in which for each pair of factors in any combination of factor values occurs only once.
- General Linear Model for a Latin Square (Graphical)In design of experiment, a Latin square is a three-factor experiment in which for each pair of factors in any combination of factor values occurs only once.
- Generalized Cochran-Mantel-Haenszel testsThe Generalized Cochran-Mantel-Haenszel test is a family of tests aimed at detecting of association between two categorical variables observed in K strata.
- Geometric DistributionA random variable x obeys the geometric distribution with parameter p (0<p<1) if P{x=k} = p(1–p)k, k=0,1,2, … .
- Geometric Distribution (Graphical)A random variable x obeys the geometric distribution with parameter p (0<p<1) if If a random variable obeys the Bernoulli distribution with probability of success p, then x might be the number of trials…
- Geometric meanThe geometric mean of n values is determined by multiplying all n values together, then taking the nth root of the product.
- Geometric Mean and Mean (comparison)The quantitative distinction between the geometric mean and the mean can be illustrated by the following table: Data set Mean Geometric Mean 1, 1, 1 1 1 1, 2, 3 2 1.6 1, 2, 1000 334 6.7 The analytical…
- Gini coefficientThe Gini coefficient is used in economics to measure income inequality. Generally speaking, it is used to measure the extent of departure from a perfectly even distribution of income.
- Gini coefficient (Graphical)The Gini coefficient is used in economics to measure income inequality. Generally speaking, it is used to measure the extent of departure from a perfectly even distribution of income.
- Gini’s Mean DifferenceN(N–1) GMD = 1 ? ij |xi–xj|; i,j = 1,…,N; i ? j .
- Goodness – of – Fit TestIt is a statistical test to determine whether there is significant difference between the observed frequency distribution and a theoretical probability distribution which is hypothesized to describe the…
- Granger CausationGranger causation is a definition of causal relation between vectors in vector time series.
H
- HadoopAs data processing requirements grew beyond the capacities of even large computers, distributed computing systems were developed to spread the load to multiple computers.
- Harmonic MeanHarmonic mean is a measure of central location. The harmonic mean of positive values is defined by the formula Let the path between two cities and be divided into parts of equal length.
- Hazard FunctionIn medical statistics, the hazard function is a relationship between a proportion and time.
- Hazard RateSee Hazard function
- HDFSHDFS is the Hadoop Distributed File System. It is designed to accommodate parallel processing on clusters of commodity hardware, and to be fault tolerant.
- HeteroscedasticityHeteroscedasticity generally means unequal variation of data, e.g. unequal variance. For special cases see heteroscedasticity in regression, heteroscedasticity in hypothesis testing
- Heteroscedasticity in hypothesis testingIn hypothesis testing, heteroscedasticity means a situation in which the variance is different for compared samples.
- Heteroscedasticity in regressionIn regression analysis, heteroscedasticity means a situation in which the variance of the dependent variable varies across the data.
- Hierarchical Cluster AnalysisHierarchical cluster analysis (or hierarchical clustering) is a general approach to cluster analysis, in which the object is to group together objects or records that are “close” to one another.
- HistogramA histogram is a graph of a dataset, composed of a series of rectangles. The width of these rectangles is proportional to the range of values in a class or bin, all bins being the same width.
- Hold-Out SampleA hold-out sample is a random sample from a data set that is withheld and not used in the model fitting process.
- HomoscedasticityHomoscedasticity generally means equal variation of data, e.g. equal variance. For special cases see homoscedasticity in regression, homoscedasticity in hypothesis testing
- Homoscedasticity in hypothesis testingIn hypothesis testing, homoscedasticity means a situation in which the variance is the same for all the compared samples.
- Homoscedasticity in regressionIn regression analysis, homoscedasticity means a situation in which the variance of the dependent variable is the same for all the data.
- Hotelling Trace CoefficientThe Hotelling Trace coefficient (also called Lawley-Hotelling or Hotelling-Lawley Trace) is a statistic for a multivariate test of mean differences between two groups.
- Hotelling-Lawley TraceSee Hotelling Trace coefficient.
- Hotelling’s T-SquareHotelling’s T-square is a statistic for a multivariate test of differences between the mean values of two groups.
- HypothesisA (statistical) hypothesis is an assertion or conjecture about the distribution of one or more random variables.
- Hypothesis TestingHypothesis testing (also called “significance testing”) is a statistical procedure for discriminating between two statistical hypotheses – the null hypothesis (H0) and the alternative hypothesis ( Ha, often…
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- Icon PlotsIcon plots are graphical tools for multivariate analysis. They provide graphical representation of observed units described by many variables.
- Image ProcessingIn image processing, the initial data are images – functions of two coordinates. Normally, images are represented in discrete form as two-dimensional arrays of image elements, or “pixels” – i.e.
- Independent EventsTwo events A and B are said to be independent if P(AB) = P(A).P(B). To put it differently, events A and B are independent if the occurrence or non-occurrence of A does not influence the occurrence of…
- Independent Random VariablesTwo or more random variables are said to be independent it their joint distribution (density) is the product of their marginal distributions (densities).
- Independent VariableSee dependent and independent variables.
- IndicatorSee manifest variable
- Inferential StatisticsInferential statistics is the body of statistical techniques that deal with the question “How reliable is the conclusion or estimate that we derive from a set of data?” The two main techniques are…
- Input variablesee dependent and independent variables
- Interaction effectAn interaction effect refers to the role of a variable in an estimated model, and its effect on the dependent variable.
- Interim MonitoringIn clinical trials of medical treatments or devices, a traditional fixed sample design establishes a fixed number of subjects or outcomes that must be observed.
- Internal Consistency ReliabilityThe internal consistency reliability of survey instruments (e.g. psychological tests), is a measure of reliability of different survey items intended to measure the same characteristic.
- Interobserver ReliabilityThe interobserver reliability of a survey instrument, like a psychological test, measures agreement between two or more subjects rating the same object, phenomenon, or concept.
- Interquartile RangeThe difference between the 3d and 1st quartiles is called the interquartile range and it is used as a measure of variability (dispersion).
- Interval ScaleAn interval scale is a measurement scale in which a certain distance along the scale means the same thing no matter where on the scale you are, but where “0” on the scale does not represent the absence of…
- Intraobserver ReliabilityIntraobserver reliability indicates how stable are responses obtained from the same respondent at different time points.
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- JackknifeThe jackknife is a general non-parametric method for estimation of the bias and variance of a statistic (which is usually an estimator) using only the sample itself.
- Joint Probability DensityA function f(x,y) is called the joint probability density of random variables X and Y if and only if for any region A on the xy-plane
- Joint Probability DistributionIf X and Y are discrete random variables, the function f(x,y) which gives the probability that X = x and Y = y for each pair of values (x,y) within the range of values of X and Y is called the joint…
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- k-Means ClusteringThe k-means clustering method is used in non-hierarchical cluster analysis. The goal is to divide the whole set of objects into a predefined number (k) of clusters.
- k-Nearest neighborK-nearest-neighbor (K-NN) is a machine learning predictive algorithm that relies on calculation of distances between pairs of records.
- k-Nearest Neighbors ClassificationThe k-nearest neighbors (k-NN) classification is a method of classification that uses a training set chosen from the data as a point of reference in classifying observations.
- k-Nearest Neighbors PredictionThe k-nearest neighbors (k-NN) prediction is a method to predict a value of a target variable in a given record, using as a reference point a training set of similar objects.
- Kalman FilterKalman filter is a class of linear filters for predicting and/or smoothing time series. The value of the time series is usually a vector in a state space.
- Kalman Filter (Equations)The basic mathematics behind the idea of Kalman filter may be described as follows – Consider, for example, a Markov chain – i.e.
- Kaplan-Meier EstimatorThe Kaplan-Meier estimator is aimed at estimation of the survival function from censored life-time data.
- Kappa StatisticKappa statistic is a generic term for several similar measures of agreement used with categorical data.
- Kolmogorov-Smirnov One-sample TestThe Kolmogorov-Smirnov one-sample test is a goodness-of-fit test, and tests whether an observed dataset is consistent with an hypothesized theoretical distribution.
- Kolmogorov-Smirnov TestSee: Kolmogorov-Smirnov one-sample test and Kolmogorov-Smirnov two-sample test
- Kolmogorov-Smirnov Two-sample TestThe Kolmogorov-Smirnov two-sample test is a test of the null hypothesis that two independent samples have been drawn from the same population (or from populations with the same distribution).
- Kruskal – Wallis TestThe Kruskal-Wallis test is a nonparametric test for finding if three or more independent samples come from populations having the same distribution.
- KurtosisKurtosis measures the “heaviness of the tails” of a distribution (in compared to a normal distribution).
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- LabelA label is a category into which a record falls, usually in the context of predictive modeling.
- Lan-Demets Spending FunctionSee alpha spending function.
- Latent Structure ModelsLatent structure models is a generic term for a broad set of categories of statistical models.
- Latent VariableA latent variable describes an unobservable construct and cannot be observed or measured directly.
- Latent Variable Growth Curve ModelsThese techniques, also called Latent Curve Models (LCM), take traditional modeling of growth curves for repeated measures data and extend it to cover the use of latent variables.
- Latent Variable ModelsLatent variable models are a broad subclass of latent structure models. They postulate some relationship between the statistical properties of observable variables (or “manifest variables”, or “indicators”)…
- Latin SquareThe Latin Square is a square array in which every letter or symbol appears exactly one in each row and in each column.
- Law Of Large NumbersAccording to the Law of Large Numbers, the probability that the proportion of successes in a sample will differ from the population proportion by less than c ( any positive constant) approaches 1 as the…
- Lawley-Hotelling TraceSee Hotelling Trace coefficient.
- Least Squares MethodIn a narrow sense, the Least Squares Method is a technique for fitting a straight line through a set of points in such a way that the sum of the squared vertical distances from the observed points to the…
- Level of a FactorIn design of experiments, levels of a factor are the values it takes on. The values are not necessarily numbers – they may be at a nominal scale, ordinal scale, etc.
- Level Of SignificanceIn hypothesis testing, you seek to decide whether observed results are consistent with chance variation under the “null hypothesis,” or, alternatively, whether they are so different that chance variability…
- Life TablesIn survival analysis, life tables summarize lifetime data or, generally speaking, time-to-event data.
- Likelihood FunctionLikelihood function is a fundamental concept in statistical inference. It indicates how likely a particular population is to produce an observed sample.
- Likelihood Function (Graphical)Likelihood function is a fundamental concept in statistical inference. It indicates how likely a particular population is to produce an observed sample.
- Likelihood Ratio TestThe likelihood ratio test is aimed at testing a simple null hypothesis against a simple alternative hypothesis.
- Likelihood Ratio Test (Graphical)The likelihood ratio test is aimed at testing a simple null hypothesis against a simple alternative hypothesis.
- Likert ScalesLikert scales are categorical ordinal scales used in social sciences to measure attitude. Measurements at Likert scales usually take on an odd number of values with a middle point, e.g.
- Lilliefors StatisticThe Lilliefors statistic is used in a goodness-of-fit test of whether an observed sample distribution is consistent with normality.
- Lilliefors test for normalityThe Lilliefors test is a special case of the Kolmogorov-Smirnov goodness-of-fit test. In the Lilliefors test, the Kolmogorov-Smirnov test is implemented using the sample mean and standard deviation as the…
- Line of RegressionThe line of regression is the line that best fits the data in simple linear regression, i.e.
- Linear FilterA linear filter is the filter whose output is a linear function of the input. Any output value of a linear filter is the weighted mean of input values.
- Linear ModelA linear model specifies a linear relationship between a dependent variable and n independent variables: y = a0 + a1 x1 + a2 x2 + ¼+ an xn, where y is the dependent variable, {xi} are independent…
- Linear Model (Graphical)A linear model specifies a linear relationship between a dependent variable and n independent variables: where y is the dependent variable, {xi} are independent variables, {ai} are parameters of the model.
- Linear RegressionLinear regression is aimed at finding the “best-fit” linear relationship between the dependent variable and independent variable(s).
- Linkage FunctionA linkage function is an essential prerequisite for hierarchical cluster analysis. Its value is a measure of the “distance” between two groups of objects (i.e.
- Local IndependenceThe local independence postulate plays a central role in latent variable models. Local independence means that all the manifest variables are independent random variables if the latent variables are…
- Log-log PlotA log-log plot represents observed units described by two variables, say x and y , as a scatter graph.
- Log-Normal DistributionA random variable X has a log-normal distribution if ln(X) is normally distributed.
- Logistic Regression1–pi Li = log pi = a + b xi, where pi is the probability of a success for given value xi of the explanatory variable X.
- Logistic Regression (Graphical)Logistic regression is used with binary data when you want to model the probability that a specified outcome will occur.
- Logit(1 – p) logit(p) = log p Logit is widely used to construct statistical models, for example in logistic regression.
- Logit and Odds RatioThe following relation between the odds ratio and logit is often used for constructing statistical models: log OR(p1, p2) = logit (p1) – logit (p2) where p1, p2 are probabilities, OR (p1, p2) is the odds…
- Logit ModelsLogit models postulate some relation between the logit of observed probabilities (not the probabilities themselves), and unknown parameters of the model.
- Loglinear modelsLoglinear models are models that postulate a linear relationship between the independent variables and the logarithm of the dependent variable, for example: log(y) = a0 + a1 x1 + a2 x2 … + aN xN where y is…
- Loglinear regressionLoglinear regression is a kind of regression aimed at finding the best fit between the data and a loglinear model.
- Longitudinal AnalysisLongitudinal analysis is concerned with statistical inference from longitudinal data
- Longitudinal DataLongitudinal data refer to observations of given units made over time. A simple example of longitudinal data is the gross annual income of, say, 1000 households from New York City for the years 1991-2000.
- Longitudinal studyLongitudinal studies are those that record data for subjects or variables over time. If a longitudinal study uses the same subjects at each point where data are recorded, it is a panel study.
- Loss FunctionA loss function specifies a penalty for an incorrect estimate from a statistical model. Typical loss functions might specify the penalty as a function of the difference between the estimate and the true…
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- Manifest VariableIn latent variable models, a manifest variable (or indicator) is an observable variable – i.e.
- Mann – Whitney U TestSee Wilcoxon – Mann – Whitney Test.
- MANOVASee Multiple analysis of variance
- Mantel-Cox TestThe Mantel-Cox test is aimed at testing the null-hypothesis that survival functions don’t differ across groups.
- Mantel-Haenszel testSee Cochran-Mantel-Haenszel test
- MapReduceIn computer science, MapReduce is a procedure that prepares data for parallel processing on multiple computers.
- Margin of ErrorA margin of error typically refers to a range within which an unknown parameter is estimated to fall, given the variation that can arise from one sample to another.
- Marginal DensityIf X and Y are continuous random variables, and f(x,y ) is the joint density of X and Y, then the marginal density of X, g(x), is given by
- Marginal DistributionIf X and Y are discrete random variables and f(x,y) is their joint probability distribution, the marginal distribution of X, g(x) is given by
- Markov ChainA Markov chain is a series of random values x1, x2, … in which the probabilities associated with a particular value xi depend only on the prior value xi-1.
- Markov Chain (Graphical)A Markov chain is a series of random values x1, x2, … in which the probabilities associated with a particular value xi depend only on the prior value .
- Markov Chain Monte Carlo (MCMC)A Markov chain is a probability system that governs transition among states or through successive events.
- Markov PropertyMarkov property means “absence of memory” of a random process – that is, independence of conditional probabilities P( U(t1 > t) | U(t) ) on values U(t2 < t).
- Markov Property (Graphical)Markov property means “absence of memory” of a random process – that is, independence of conditional probabilities on values U(t2 < t).
- Markov Random FieldSee Markov Chain, Random Field.
- Maximum Likelihood EstimatorThe method of maximum likelihood is the most popular method for deriving estimators – the value of the population parameter T maximizing the likelihood function is used as the estimate of this parameter.
- Maximum Likelihood Estimator (Graphical)The method of maximum likelihood is the most popular method for deriving estimators – the value of the population parameter T maximizing the likelihood function is used as the estimate of this parameter.
- MeanFor a population or a sample, the mean is the arithmetic average of all values. The mean is a measure of central tendency or location.
- Mean DeviationSee Average deviation
- Mean Score StatisticThe mean score statistic is one of the statistics used in the generalized Cochran-Mantel-Haenszel tests.
- Mean Squared ErrorThe mean squared error is a measure of performance of a point estimator. It measures the average squared difference between the estimator and the parameter.
- Mean Values (Comparison)The numerical example below illustrates basic properties of various descriptive statistics with “mean” in their name, like the arithmetic mean, the trimmed mean, the geometric mean, the harmonic mean, and…
- Measurement ErrorThe measurement error is the deviation of the outcome of a measurement from the true value.
- MedianIn a population or a sample, the median is the value that has just as many values above it as below it.
- Median FilterThe median filter is a robust filter. Median filters are widely used as smoothers for image processing, as well as in signal processing and time series processing.
- Meta-analysisMeta-analysis takes the results of two or more studies of the same research question and combines them into a single analysis.
- Minimax Decision RuleA minimax decision rule has the smallest possible maximum risk. All other decision rules will have a higher maximum risk.
- Missing Data Imputation“Imputing missing data” is a process by which the missing values in a data set are estimated from the remaining data, for the purpose of allowing statistical procedures to be performed on a complete data set.
- ModeThe mode is a value that occurs with the greatest frequency in a population or a sample. It could be considered as the single value most typical of all the values.
- Moment Generating FunctionThe moment generation function is associated with a probability distribution. The moment generating function can be used to generate moments.
- MomentsFor a random variable x, its Nth moment is the expected value of the Nth power of x, where N is a positive integer.
- Monte Carlo SimulationMonte Carlo simulation is simulation of a random phenomena using pseudo-random numbers. This type of simulation is widely used in practical statistics, e.g.
- Moving Average (MA) ModelsMoving average (MA) models are used in time series analysis to describe stationary time series.
- MulticollinearityIn regression analysis, multicollinearity refers to a situation of collinearity of independent variables, often involving more than two independent variables, or more than one pair of collinear variables.
- Multidimensional ScalingMultidimensional scaling (MDS) is an approach to multivariate analysis aimed at producing a spatial or geometrical representation of complex data.
- Multiple analysis of covariance (MANCOVA)Multiple analysis of covariance (MANCOVA) is similar to multiple analysis of variance (MANOVA), but allows you to control for the effects of supplementary continuous independent variables – covariates.
- Multiple analysis of variance (MANOVA)MANOVA is a technique which determines the effects of independent categorical variables on multiple continuous dependent variables.
- Multiple ComparisonMultiple comparisons are used in the same context as analysis of variance (ANOVA) – to check whether there are differences in population means among more than two populations.
- Multiple Least Squares RegressionMultiple least squares regression is a special (and the most common) type of multiple regression.
- Multiple looks<b Multiple looks: In a classic statistical experiment, treatment(s) and placebo are applied to randomly assigned subjects, and, at the end of the experiment, outcomes are compared.
- Multiple RegressionMultiple (linear) regression is a regression technique aimed at finding a linear relationship between the dependent variable and multiple independent variables.
- Multiple Regression (Graphical)Multiple (linear) regression is a regression technique aimed at finding a linear relationship between the dependent variable and multiple independent variables.
- Multiple TestingSee Multiple comparison.
- Multiplicative ErrorA multiplicative error is proportional to the true value of the quantity being measured. An example of a multiplicative error is when electronic scales provide readings 1% higher than the true weight – i.e.
- MultivariateMultivariate analysis involves more than one variable of interest.
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- Naive bayes classifierA full Bayesian classifier is a supervised learning technique that assigns a class to a record by finding other records with attributes just like it has, and finding the most prevalent class among them.
- Natural LanguageA natural language is what most people outside the field of computer science think of as just a language (Spanish, English, etc.).
- Nearest Neighbor ClusteringThe nearest neighbor clustering is a synonym for single linkage clustering.
- Negative BinomialThe negative binomial distribution is the probability distribution of the number of Bernoulli (yes/no) trials required to obtain r successes.
- Netflix PrizeThe Netflix prize was a famous early application of crowdsourcing to predictive modeling. In 2006, Netflix published customer movie rating data and challenged analysts to come up with a predictive model…
- Neural NetworkA neural network (NN) is a network of many simple processors (“units”), each possibly having a small amount of local memory.
- NodeA node is an entity in a network. In a social network, it would be a person. In a digital network, it would be a computer or device.
- NoiseThe noise is the component of the observed data (e.g. of a time series) that is random and carries no useful information.
- Nominal ScaleA nominal scale is really a list of categories to which objects can be classified. For example, people who receive a mail order offer might be classified as “no response,” “purchase and pay,” “purchase but…
- Non-parametric RegressionNon-parametric regression methods are aimed at describing a relationship between the dependent and independent variables without specifying the form of the relationship between them a priori.
- Nonlinear FilterA nonlinear filter is the filter whose output is a nonlinear function of the input. By definition, any filter that is not a linear filter is a nonlinear filter.
- Nonparametric ANOVA StatisticSee Mean Score Statistic.
- Nonparametric TestsIn statistical inference procedures (hypothesis tests and confidence intervals), nonparametric procedures are those that are relatively free of assumptions about population parameters.
- Nonrecursive FilterIn nonrecursive filters, the output at the moment is a function of only input values corresponding to the time moments : A complementary concept is recursive filter.
- Nonstationary time seriesA time series x_t is called to be nonstationary if its statistical properties depend on time.
- Normal DistributionThe normal distribution is a probability density which is bell-shaped, symmetrical, and single peaked.
- NormalityNormality is a property of a random variable that is distributed according to the normal distribution.
- Normality TestsNormality tests are tests of whether a set of data is distributed in a way that is consistent with a normal distribution.
- NoSQLA NoSQL database is distinguished mainly by what it is not – it is not a structured relational database format that links multiple separate tables.
- Null HypothesisIn hypothesis testing, the null hypothesis is the one you are hoping can be disproven by the observed data.
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- Odds RatioP2/(1–P2) q = P1/(1–P1) . If P1 and P2 are equal, the odds ratio is equal to 1. If the symbols do not display properly, try the graphic version of this page
- Odds Ratio (Graphical)The odds ratio compares two probabilities (or proportions) P1 and P2 in the following way: If P1 and P2 are equal, the odds ratio is equal to 1.
- Omega-squareOmega-square is a synonym for the coefficient of determination.
- One-sided TestOne-sided test is a synonym for one-tailed test. See 2-Tailed vs. 1-Tailed Tests
- Order StatisticsThe order statistics of a random sample X1, X2, . . ., Xn are the sample values placed in ascending order.
- Ordered categorical dataCategorical variables are non-numeric “category” variables, e.g. color. Ordered categorical variables are category variables that have a quantitative dimension that can be ordered but is not on a regular scale.
- Ordinal ScaleAn ordinal scale is a measurement scale that assigns values to objects based on their ranking with respect to one another.
- Ordinary Least Squares RegressionOrdinary least squares regression is a special (and the most common) kind of ordinary linear regression.
- Ordinary Linear RegressionSee: simple linear regression
- Orthogonal Least SquaresIn ordinary least squares, we try to minimize the sum of the vertical squared distances between the observed points and the fitted line.
- Outcome variablesee dependent and independent variables
- OutlierSometimes a set of data will have one or more items with unusually large or unusually small values.
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- p-valueThe p-value is the probability that the null model could, by random chance variation, produce a sample as extreme as the observed sample (as measured by some sample statistic of interest.)
- Paired Replicates DataPaired replicates is the simplest form of repeated measures data, when only two measurements are made for each experimental unit.
- Panel DataA panel data set contains observations on a number of units (e.g. subjects, objects) belonging to different clusters (panels) over time.
- Panel studyA panel study is a longitudinal study that selects a group of subjects then records data for each member of the group at various points in time.
- Parallel DesignIn randomized trials, a parallel design is one in which subjects are randomly assigned to treatments, which then proceed in parallel with each group.
- ParameterA Parameter is a numerical value that describes one of the characteristics of a probability distribution or population.
- Parametric TestsIn statistical inference procedures (hypothesis tests and confidence intervals), parametric procedures are those that incorporate assumptions about population parameters.
- Path AnalysisPath analysis is a method for causal modeling. Consider the simple case of two independent variables x1 and x2 and one dependent variable.
- Path coefficientsIn path analysis and structural equation modeling a path coefficient is the partial correlation coefficient between the dependent variable and an independent variable, adjusted for other independent variables.
- Pearson correlation coefficientSee correlation coefficient.
- PercentileIn a population or a sample, the Pth percentile is a value such that at least P percent of the values take on this value or less and at least (100-P) percent of the values take on this value or more.
- Permutation TestsA permutation test involves the shuffling of observed data to determine how unusual an observed outcome is.
- Pie Icon PlotsPie icon plots are a sub-class of icon plots. Each unit or observation is represented by a circle with colored “pies slices” corresponding to variables – the angular size of a slice of pie is proportional…
- Pivotal StatisticA statistic is said to be pivotal if its sampling distribution does not depend on unknown parameters.
- Poisson Distributionk! p(x=k) = lk e–l, k=0,1,2,� (where k! = 1 x 2 x … x k). Both the mean and the variance of Poisson distribution are equal to l.
- Poisson Distribution (Graphical)Poisson distribution is a discrete distribution, completely characterized by one parameter : (where k!
- Poisson ProcessA Poisson process is a random function U(t) which describes the number of random events in an interval [0,t] of time or space.
- Poisson Process (Graphical)A Poisson process is a random function U(t) which describes the number of random events in an interval [0,t] of time or space.
- Polygon Icon PlotsPolygon icon plots are a subclass of circular icon plots in which the rays tend to form a polygon.
- PolynomialA polynomial of order is a function described by the following expression: where are coefficients of the polynomial.
- PopulationA population is a large set of objects of a similar nature – e.g. human beings, households, readings from a measurement device – which is of interest as a whole.
- Post-hoc testsPost-hoc tests (or post-hoc comparison tests) are used at the second stage of the analysis of variance (ANOVA) or multiple analysis of variance (MANOVA) if the null hypothesis is rejected.
- Posterior ProbabilityPosterior probability is a revised probability that takes into account new available information.
- Power MeanA power mean of order of a set of values is defined by the following expression: The family of power mean statistics is often called the generalized mean – because, for different values of the parameter ,…
- Power of a Hypothesis TestThe power of hypothesis test is a measure of how effective the test is at identifying (say) a difference in populations if such a difference exists.
- Power SpectrumThe power spectrum of a stationary random process or a stationary time series is the average of the square of the amplitude of the Fourier spectrum: where is the amplitude spectrum of the realization of the…
- PrecisionPrecision is the degree of accuracy with which a parameter is estimated by an estimator. Precision is usually measured by the standard deviation of the estimator and is known as the standard error.
- Predicting FilterPredicting filters are filters that estimate the next value in a time series from the known previous values.
- Prediction vs. ExplanationWith the advent of Big Data and data mining, statistical methods like regression and CART have been repurposed to use as tools in predictive modeling.
- Predictive ModelingPredictive modeling is the process of using a statistical or machine learning model to predict the value of a target variable (e.g.
- Predictive ValidityThe predictive validity of survey instruments and psychometric tests is a measure of agreement between results obtained by the evaluated instrument and results obtained from more direct and objective…
- predictorsee dependent and independent variables
- Predictor VariablePredictor variable is a synonym for independent variable.
- Principal Component AnalysisThe purpose of principal component analysis is to derive a small number of linear combinations (principal components) of a set of variables that retain as much of the information in the original variables…
- Prior and posteriorBayesian statistics typically incorporates new information (e.g. from a diagnostic test, or a recently drawn sample) to answer a question of the form “What is the probability that…” The answer to this…
- Prior and posterior probability (difference)Consider a population where the proportion of HIV-infected individuals is 0.01. Then, the prior probability that a randomly chosen subject is HIV-infected is Pprior = 0.01 .
- Prior ProbabilitySee A Priori Probability.
- ProbitProbit is a nonlinear function of probability p: probit(p) = F–1(p) where F–1() is the function inverse to the cumulative distribution function F() of the standard normal distribution.
- Proportional Hazard ModelProportional hazard model is a generic term for models (particularly survival models in medicine) that have the form L(t | x1, x2, ¼, xn) = h(t) exp(b1 x1 + ¼+ bn xn), where L is the hazard function…
- Proportional Hazard Model (Graphical)Proportional hazard model is a generic term for models (particularly survival models in medicine) that have the form where L is the hazard function or hazard rate, {xi} are covariates, {bi} are coefficients…
- Prospective Versus RetrospectiveProspective vs. Retrospective A prospective study is one that identifies a scientific (usually medical) problem to be studied, specifies a study design protocol (e.g.
- Pruning the tree<b Pruning the tree: Classification and regression trees, applied to data with known values for an outcome variable, derive models with rules like “If taxable income <$80,000, if no Schedule C income, if…
- Pseudo-Random NumbersPseudo-random numbers are produced by recursive algorithms – i.e. the current number is calculated from one or a greater number of previous numbers.
- Psychological TestingSee psychometrics.
- PsychometricsPsychometrics or psychological testing is concerned with quantification (measurement) of human characteristics, behavior, performance, health, etc., as well as with design and analysis of studies based on…
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- Quadratic MeanThe quadratic mean is a special case of the power mean statistics , corresponding to the value of the parameter.
- QuartileThe 1st, 2nd, and 3d quartiles are the 25th, 50th, and 75th percentiles respectively.
- Quasi-experimentIn social science research, particularly in the qualitative literature on program evaluation, the term “quasi-experiment” refers to studies that do not involve the application of treatments via random…
- Queuing ProcessQueuing process is a class of random process es describing phenomena of queue formation. The term “queue” here is an abstract entity, which reflects the most common features of various types of real-life…
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- R-squaredSee Coefficient of determination
- Random ErrorThe random error is the fluctuating part of the overall error that varies from measurement to measurement.
- Random FieldA random field describes an experiment with outcomes being functions of more than one continuous variable, for example U(x,y,z), where x, y, and z are coordinates in space.
- Random NumbersRandom numbers are the numbers produced by a truly random mechanism (in contrast to pseudo-random numbers).
- Random ProcessA random process describes an experiment with outcomes being functions of a single continuous variable (e.g.
- Random SamplingRandom sampling is a method of selecting a sample from a population in which all the items in the population have an equal chance of being chosen in the sample.
- Random SeriesA random series describes an experiment with outcomes being functions of an integer argument: U1, U2, … (or, simply, sequences of random values – 1st value, 2nd value, etc).
- Random VariableA random variable is a variable that takes different real values as a result of the outcomes of a random event or experiment.
- Random WalkA random walk is a process of random steps, motions, or transitions. It might be in one dimension (movement along a line), in two dimensions (movements in a plane), or in three dimensions or more.
- Randomization TestSee permutation tests.
- RangeRange is a measure of dispersion. It is defined as the difference between the highest and the lowest values.
- Rank Correlation CoefficientRank correlation is a method of finding the degree of association between two variables. The calculation for the rank correlation coefficient the same as that for the Pearson correlation coefficient, but is…
- Ratio ScaleA ratio scale is a measurement scale in which a certain distance along the scale means the same thing no matter where on the scale you are, and where “0” on the scale represents the absence of the thing…
- Reciprocal AveragingReciprocal averaging is a widely used algorithm for correspondence analysis. The correspondence analysis itself is sometimes also called reciprocal averaging.
- Rectangular FilterThe rectangular filter is the simplest linear filter; it is usually used as a smoother. The output of the rectangular filter at the time moment is the arithmetic mean of the input values corresponding to…
- Recursive FilterIn recursive filters, the output at the moment is a function of the output values at the previous moments and, probably, of the input values.
- RegressionSee regression analysis.
- Regression AnalysisRegression analysis provides a “best-fit” mathematical equation for the relationship between the dependent variable (response) and independent variable(s) (covariates).
- Regression TreesRegression trees is one of the CART techniques. The main distinction from classification trees (another CART technique) is that the dependent variable is continuous.
- RegularizationRegularization refers to a wide variety of techniques used to bring structure to statistical models in the face of data size, complexity and sparseness.
- Rejection RegionSee Acceptance region
- Relative Efficiency (of tests)The relative efficiency of two tests is a measure of the relative power of two tests. Suppose tests 1 and 2 are tests for the same null-hypothesis and at the same significance level “alpha” (probability of…
- Relative Frequency DistributionA relative frequency distribution is a tabular summary of a set of data showing the relative frequency of items in each of several non-overlapping classes.
- ReliabilityReliability characterises the capability of a device, unit, procedure to perform without fault.
- Reliability (in Survey Analysis)In survey analysis, e.g. in psychometrics, reliability is a measure of reproducibility of the survey instrument or test.
- RepeatabilityRepeatability is the variation of outcomes of an experiment carried out in the same conditions, e.g.
- Repeated Measures DataRepeated measures (or repeated measurements) data are usually obtained from multiple measurements of a response variable.
- ReplicateA replicate is the outcome of an experiment or observation obtained in course of its replication.
- ReplicationIn statistics, replication is repetition of an experiment or observation in the same or similar conditions.
- ReproducibilityReproducibility is the variation of outcomes of an experiment carried out in conditions varying within a typical range, e.g.
- ResamplingSee bootstrapping and permutation tests
- ResidualsResiduals are differences between the observed values and the values predicted by some model.
- ResistanceResistance, used with respect to sample estimators, refers to the sensitivity of the estimator to extreme observations.
- ResponseIn design of experiments, response is a dependent variable. Its values are measured for all subjects, and the question of primary interest is how factors affect the response.
- Response Variablesee dependent and independent variables
- RMSSee Root Mean Square.
- RMSERMSE is root mean squared error. In predicting a numerical outcome with a statistical model, predicted values rarely match actual outcomes exactly.
- Robust FilterA robust filter is a filter that is not sensitive to input noise values with extremely large magnitude (e.g.
- RobustnessMany statistical methods (particularly classical inference methods) rely upon assumptions about the distribution of the population the sample is drawn from.
- Root Mean SquareN 1 N ? i=1 xi2 RMS is a statistical measure of departure from the null value. If the symbols do not display properly, try the graphic version of this page
- Root Mean Square (Graphical)Root mean square (RMS) of a set of values xi, i=1,…N is the square root of the mean of the squares of the values: RMS is a statistical measure of departure from the null value.
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- SampleA sample is a portion of the elements of a population. A sample is chosen to make inferences about the population by examining or measuring the elements in the sample.
- Sample Size CalculationsSample size calculations typically arise in significance testing, in the following context: how big a sample size do I need to identify a significant difference of a certain size?
- Sample SpaceThe set of all possible outcomes of a particular experiment is called the sample space for the experiment.
- Sample SurveyIn a sample survey, a sample of units drawn from the population of interest is analyzed. A related concept is the census survey.
- SamplingSampling is a process of drawing a sample from a population. Sampling may be performed from both real and hypothetical populations.
- Sampling DistributionWhen a sample is drawn, some summary value (called a statistic) is usually computed. For example, the sample mean and the sample variance are two statistics.
- Sampling FrameSampling frame (synonyms: “sample frame”, “survey frame”) is the actual set of units from which a sample has been drawn: in the case of a simple random sample, all units from the sampling frame have an…
- Scale Invariance (of Measures)Scale invariance is a property of descriptive statistics. If a statistic is scale-invariant, it has the following property for any sample and any non-negative value : (1) or, in mathematically equivalent…
- Scatter GraphsA scatter graph shows the joint distribution of observed values of two variables. Each pair of values is shown as a point on X-Y plane with coordinates (Xi,Yi), where Xi and Yi are the values of the first…
- Seasonal AdjustmentThe seasonal adjustment is used in time series analysis to remove a periodic component with the known period from the observed time series.
- Seasonal DecompositionThe seasonal decomposition is a method used in time series analysis to represent a time series as a sum (or, sometimes, a product) of three components – the linear trend, the periodic (seasonal) component,…
- Seemingly Unrelated Regressions (SUR)Seemingly unrelated regressions (SUR) is a class of multivariate regression ( multiple regression) models, normally belonging to the sub-class of linear regression models.
- Self-Controlled DesignIn randomized trials, a self-controlled design is one in which results are measured in each subject before and after treatment.
- SensitivitySensitivity (of a medical diagnostic test for a disease) is the probability that the test is positive for a person with the disease.
- Sequential Icon PlotsSequential icon plots (or column icon plots) are a category of icon plots. For each unit, variables are represented as a sequence of bars with the height reflecting the value of the corresponding variable.
- Serial CorrelationIn analysis of time series, the Nth order serial correlation is the correlation between the current value and the Nth previous value of the same time series.
- Shift Invariance (of Measures)Shift invariance is a property of descriptive statistics. If a statistic is shift-invariant, it possesses the following property for any data set : or, in equivalent form In other words, if a statistic is…
- Sign TestThe sign test is a nonparametric test used with paired replicates to test for the difference between the 1st and the 2nd measurement in a group of “subjects”.
- SignalThe signal is the component of the observed data (e.g. of a time series) that carries useful information.
- Signal ProcessingSignal processing is a branch of applied statistics concerned with analysis of functions of time that take on scalar or vector values.
- Significance TestingSee Hypothesis Testing
- Similarity MatrixSimilarity matrix is the opposite concept to the distance matrix. The elements of a similarity matrix measure pairwise similarities of objects – the greater similarity of two objects, the greater the value…
- Simple Linear RegressionThe simple linear regression is aimed at finding the “best-fit” values of two parameters – A and B in the following regression equation: Yi = A Xi + B + Ei, i=1,¼,N where Yi, Xi, and Ei are the values of…
- Simple Linear Regression (Graphical)The simple linear regression is aimed at finding the “best-fit” values of two parameters – A and B in the following regression equation: where Yi, Xi, and Ei are the values of the dependent variable, of the…
- SimulationIn general, simulation is modelling of a process or phenomenon. In statistics, Monte Carlo simulation is often used to model outcomes of a random experiment.
- Single Linkage ClusteringThe single linkage clustering method (or the nearest neighbor method) is a method of calculating distance between clusters in hierarchical cluster analysis.
- SingularityIn regression analysis, singularity is the extreme form of multicollinearity – when a perfect linear relationship exists between variables or, in other terms, when the correlation coefficient is equal to…
- Six-SigmaSix sigma means literally six standard deviations. The phrase refers to the limits drawn on statistical process control charts used to plot statistics from samples taken regularly from a production process.
- SkewnessSkewness measures the lack of symmetry of a probability distribution. A curve is said to be skewed to the right (or positively skewed) if it tails off toward the high end of the scale (right tail longer…
- Smoother (Example)A simple example of a smoother is the moving average procedure. It is based on averaging elements closest in time to the current time.
- Smoother (Smoothing Filter)Smoothers, or smoothing filters, are algorithms for time-series processing that reduce abrupt changes in the time-series and make it look smoother.
- SmoothingSmoothing is a class of time series processing which is intended to reduce noise and to preserve the signal itself.
- Social Network AnalyticsNetwork analytics applied to connections among humans. Recently it has come also to encompass the analysis of web sites and internet services like Facebook.
- SparkSpark is a second generation computing environment that sits on top of a Hadoop system, supporting the workflows that leverage a distributed file system.
- Spatial FieldA spatial field is a function of spatial variables , or in 3D cases. A spatial field is named a “scalar field” if the function takes on scalar values.
- SpecificitySpecificity (of a medical diagnostic test for a disease) is the probability that the test will come out negative for a person without the disease.
- Spectral AnalysisSpectral analysis is concerned with estimation of the spectrum of a stationary random process or a stationary time series from the observed realization(s) of the process (or series).
- SpectrumSee Fourier spectrum and power spectrum.
- SplineA spline is a continuous function which coincides with a polynomial on every subinterval of the whole interval on which is defined.
- Split-Halves MethodIn psychometric surveys, the split-halves method is used to measure the internal consistency reliability of survey instruments, e.g.
- SQLSQL stands for structured query language, a high level language for querying relational databases, extracting information.
- Standard DeviationThe standard deviation is a measure of dispersion. It is the positive square root of the variance.
- Standard errorThe standard error measures the variability of an estimator (or sample statistic) from sample to sample.
- Standard Normal DistributionThe standard normal distribution is the normal distribution where the mean is zero and the standard deviation is one.
- Standard ScoreThe standard score of an observation is the number of standard deviation units it is above or below the mean.
- Standardized Mean DifferenceThe standardized mean difference is the difference between two normalized means – i.e. the mean values divided by an estimate of the within-group standard deviation.
- StanineA stanine is a “standard ninth,” an interval used in dividing school test results into (more or less) ninths.
- Star Icon PlotsStar icon plots are a subclass of circular icon plots in which the rays tend to form a star.
- State SpaceState space is an abstract space representing possible states of a system. A point in the state space is a vector of the values of all relevant parameters of the system.
- Stationary time seriesA time series x(t); t=1,… is called to be stationary if its statistical properties do not depend on time t .
- Statistic1. A number measuring something 2. A measure calculated from a sample of data. Contrast “statistic” (drawn from a sample) with “parameter,” which is a characteristic of a population.
- Statistical SignificanceOutcomes to an experiment or repeated events are statistically significant if they differ from what chance variation might produce.
- Statistical TestA statistical test is a procedure for statistical hypothesis testing. The outcome of a statistical test is a decision to reject or accept the null hypothesis for given probability of type I error.
- Statistics1. A collection of numerical data that measure something. 2. The science of recording, organizing, analyzing and reporting quantitative information.
- StemmingIn processing unstructured text, stemming is the process of converting multiple forms of the same word into one stem, to simplify the task of analyzing the processed text.
- Step-wise RegressionStep-wise regression is one of several computer-based iterative variable-selection procedures.
- Stochastic ProcessStochastic process is a synonym for random process.
- Stratified SamplingStratified sampling is a method of random sampling. In stratified sampling, the population is first divided into homogeneous groups, also called strata.
- Strip transectA strip transect is a small subsection of a geographically-defined study area, typically chosen randomly.
- Structural Equation ModelingStructural equation modeling includes a broad range of multivariate analysis methods aimed at finding interrelations among the variables in linear models by examining variances and covariances of the variables.
- Structured vs. unstructured dataStructured data is data that is in a form that can be used to develop statistical or machine learning models (typically a matrix where rows are records and columns are variables or features).
- Sufficient StatisticSuppose X is a random vector with probability distribution (or density) P(X | V), where V is a vector of parameters, and Xo is a realization of X.
- Sufficient Statistic (Graphical)Suppose X is a random vector with probability distribution (or density) P(X | V), where V is a vector of parameters, and Xo is a realization of X.
- Sun Ray PlotsSun ray plots are a subclass of circular icon plots in which the rays tend to form a circle.
- Support Vector MachinesSupport vector machines are used in data mining (predictive modeling, to be specific) for classification of records, by learning from training data.
- SurveyStatistical surveys are general methods to gather quantitative information about a particular population.
- Survival AnalysisSurvival analysis is concerned with “time-to-event” data. In medical statistics, the data are often in the form of “time-to-death”.
- Survival FunctionIn medical statistics, the survival function is a relationship between a proportion and time.
- Systematic ErrorSystematic error is the error that is constant in a series of repetitions of the same experiment or observation.
- Systematic SamplingSystematic sampling is a method of random sampling. The elements to be sampled are selected at a uniform interval that is measured in time, order, or space.
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- t-distributionA continuous distribution, with single peaked probability density symmetrical around the null value and a bell-curve shape.
- t-distribution (Graphical)A continuous distribution, with single peaked probability density symmetrical around the null value and a bell-curve shape.
- t-statisticT-statistic is a statistic whose sampling distribution is a t-distribution. where and are the mean and the standard deviation of the sample.
- t-statistic (Graphical)T-statistic is a statistic whose sampling distribution is a t-distribution. where and are the mean and the standard deviation of the sample.
- t-testA t-test is a statistical hypothesis test based on a test statistic whose sampling distribution is a t-distribution.
- Target VariableSee dependent and independent variables
- Test SetA test set is a portion of a data set used in data mining to assess the likely future performance of a single prediction or classification model that has been selected from among competing models, based on…
- Test-Retest ReliabilityThe test-retest reliability of a survey instrument, like a psychological test, is estimated by performing the same survey with the same respondents at different moments of time.
- The Tukey Mean-Difference PlotThe Tukey mean-difference plot is a scatter graph produced not for (x,y) values themselves, but for modified coordinates (X,Y) 2 X = (x+y) , Y = y–x.
- Time SeriesTime series data are measurements of a variable taken at regular intervals over time. Time series are represented as sequences of values like x(1), x(2), … .
- Time Series AnalysisTime series analysis is a branch of statistics dealing with data represented as time series.
- Time-series dataSee longitudinal data
- TokenizationIn processing unstructured text, tokenization is the step by which the character string in a text segment is turned into units – tokens – for further analysis.
- Training SetA training set is a portion of a data set used to fit (train) a model for prediction or classification of values that are known in the training set, but unknown in other (future) data.
- TransformationTransformation is the conversion of a data set into a transformed data set by the application of a function.
- Triangular FilterThe triangular filter is a linear filter that is usually used as a smoother. The output of the rectangular filter at the moment is the weighted mean of the input values at the adjacent moments of discrete…
- Trimmed MeanThe trimmed mean is a family of measures of central tendency. The -trimmed mean of of values is computed by sorting all the values, discarding % of the smallest and % of the largest values, and computing…
- TruncationTruncation, generally speaking, means to shorten. In statistics it can mean the process of limiting consideration or analysis to data that meet certain criteria (for example, the patients still alive at a…
- Tukey’s HSD (Honestly Significant Differences) TestThis test is used for testing the significance of unplanned pairwise comparisons. When you do multiple significance tests, the chance of finding a “significant” difference just by chance increases.
- Two-Tailed TestA two-tailed test is a hypothesis test in which the null hypothesis is rejected if the observed sample statistic is more extreme than the critical value in either direction (higher than the positive…
- Type I ErrorIn a test of significance, Type I error is the error of rejecting the null hypothesis when it is true — of saying an effect or event is statistically significant when it is not.
- Type II ErrorIn a test of significance, Type II error is the error of accepting the null hypothesis when it is false — of failing to declare a real difference as statistically significant.
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- Uncertainty and StatisticsA main goal of statistics is to quantify or measure uncertainty; this branch of statistics is called “inferential statistics.” classical statistics measures uncertainty using fundamental concepts and…
- Uniform DistributionThe uniform distribution describes probabilistic properties of a continuous random variable that is equally likely to take any value within an interval , and never takes on values outside this interval.
- UnivariateUnivariate analysis involves a single variable of interest.
- Uplift or Persuasion ModelingA combination of treatment comparisons (e.g. send a sales solicitation, or send nothing) and predictive modeling to determine which cases or subjects respond (e.g.
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- Validation SampleThe validation sample is the subset of the data available to a data mining routine used as the validation set.
- Validation SetA validation set is a portion of a data set used in data mining to assess the performance of prediction or classification models that have been fit on a separate portion of the same data set (the training set).
- ValidityValidity characterises the extent to which a measurement procedure is capable of measuring what it is supposed to measure.
- Variable-Selection ProceduresIn regression analysis, variable-selection procedures are aimed at selecting a reduced set of the independent variables – the ones providing the best fit to the model.
- Variable-Selection Procedures (Graphical)In regression analysis, variable-selection procedures are aimed at selecting a reduced set of the independent variables – the ones providing the best fit to the model.
- Variables (in design of experiments)Many statistical methods rest on a statistical model which states a relationship Y = f(X1,..,XN) between a dependent variable (Y) and independent variable(s) X1,…,XN.
- VarianceVariance is a measure of dispersion. It is the average squared distance between the mean and each item in the population or in the sample.
- Variance/Mean RatioVariance/mean ratio (VMR) is used to characterize the distribution of events or objects in time or space.
- Variance/Mean Ratio TestThe variance/mean ratio (VMR) test is a statistical test used to test the null hypothesis that the variance/mean ratio is 1.0.
- VariateThe term “variate” is often used as synonym for “variable”. Some definitions require that variate values be numeric.
- Vector Autoregressive ModelsVector autoregressive models describe statistical properties of vector time series. Vector autoregressive models generalize the models used in ordinary autoregression.
- Vector time seriesVector time series are a natural generalization of ordinary (scalar) time series. Vector time series are measurements of a vector variable taken at regular intervals over time.
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- Ward’s LinkageWard’s linkage is a method for hierarchical cluster analysis. The idea has much in common with analysis of variance (ANOVA).
- Weighted KappaWeighted kappa is a measure of agreement for Categorical data. It is a generalization of the Kappa statistic to situations in which the categories are not equal in some respect – that is, weighted by an…
- Weighted MeanThe weighted mean is a measure of central tendency. The weighted mean of a set of values is computed according to the following formula: where are non-negative coefficients, called “weights”, that are…
- Weighted Mean (Calculation)To simplify calculation of the weighted mean, weights are often standardized to make their sum equal to the unit value, i.e.
- White Hat BiasWhite Hat Bias is bias leading to distortion in, or selective presentation of, data that is considered by investigators or reviewers to be acceptable because it is in the service of righteous goals.
- White NoiseThe white noise is a stationary time series or a stationary random process with zero autocorrelation.
- Wilcoxon – Mann – Whitney U TestThe Wilcoxon-Mann-Whitney test uses the ranks of data to test the hypothesis that two samples of sizes m and n might come from the same population.
- Wilcoxon Rank SumsWilcoxon rank sums are two statistics T+ and T– computed from paired replicates data. Suppose we have two sets of pairs of measurements (xi,yi), i=1,…,N for each of N experimental units.
- Wilcoxon Signed Ranks TestThe Wilcoxon signed ranks test is aimed at testing a null hypothesis from paired replicates data – that both treatments are equivalent.
- Wilks’s LambdaWilks’s lambda is a general test statistic used in multivariate tests of mean differences among more than two groups.
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- Z scores z = x – m , where x is the observation itself, m is the mean of the distribution, s is the standard deviation of the distribution If the symbols do not display properly, try the graphic version of this page
- Z score (Graphical)where x is the observation itself, is the mean of the distribution, is the standard deviation of the distribution
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