General linear model that blends ANOVA and regression
"Ancova" redirects here. For the moth genus, see Ancova (moth).
Analysis of covariance (ANCOVA) is a general linear model that blends ANOVA and regression. ANCOVA evaluates whether the means of a dependent variable (DV) are equal across levels of one or more categorical independent variables (IV) and across one or more continuous variables. For example, the categorical variable(s) might describe treatment and the continuous variable(s) might be covariates or nuisance variables; or vice versa. Mathematically, ANCOVA decomposes the variance in the DV into variance explained by the CV(s), variance explained by the categorical IV, and residual variance. Intuitively, ANCOVA can be thought of as 'adjusting' the DV by the group means of the CV(s).[1]
The ANCOVA model assumes a linear relationship between the response (DV) and covariate (CV):
In this equation, the DV, is the jth observation under the ith categorical group; the CV, is the jth observation of the covariate under the ith group. Variables in the model that are derived from the observed data are (the grand mean) and (the global mean for covariate ). The variables to be fitted are (the effect of the ith level of the categorical IV), (the slope of the line) and (the associated unobserved error term for the jth observation in the ith group).
Under this specification, the categorical treatment effects sum to zero The standard assumptions of the linear regression model are also assumed to hold, as discussed below.[2]
^Keppel, G. (1991). Design and analysis: A researcher's handbook (3rd ed.). Englewood Cliffs: Prentice-Hall, Inc.
^Montgomery, Douglas C. "Design and analysis of experiments" (8th Ed.). John Wiley & Sons, 2012.
and 26 Related for: Analysis of covariance information
Analysisofcovariance (ANCOVA) is a general linear model that blends ANOVA and regression. ANCOVA evaluates whether the means of a dependent variable...
Multivariate analysisofcovariance (MANCOVA) is an extension ofanalysisofcovariance (ANCOVA) methods to cover cases where there is more than one dependent...
Covariance in probability theory and statistics is a measure of the joint variability of two random variables. The sign of the covariance, therefore,...
and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square...
related to canonical correlation analysis (CCA). CCA defines coordinate systems that optimally describe the cross-covariance between two datasets while PCA...
the variance-covariance matrix implied by the proposed factor analysis model and R {\displaystyle R} is the observed variance-covariance matrix. That...
discriminant analysis (QDA). LDA instead makes the additional simplifying homoscedasticity assumption (i.e. that the class covariances are identical...
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called...
Estimation ofcovariance matrices Important publications in multivariate analysis Multivariate testing in marketing Structured data analysis (statistics)...
statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation ofcovariance matrices then deals...
Alignments of random points Almost surely Alpha beta filter Alternative hypothesis Analyse-it – software Analysisof categorical data Analysisofcovariance Analysis...
Bivariate analysis is one of the simplest forms of quantitative (statistical) analysis. It involves the analysisof two variables (often denoted as X...
MANOVA is a generalized form of univariate analysisof variance (ANOVA), although, unlike univariate ANOVA, it uses the covariance between outcome variables...
canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have...
discrimination threshold) of the detection probability in the y-axis versus the CDF of the false positive probability on the x-axis. ROC analysis provides tools...
one or both are not) and covariance (which reflects the scale variables are measured on). The slope, in regression analysis, also reflects the relationship...
i\leq k} and 1 ≤ j ≤ k {\displaystyle 1\leq j\leq k} . The inverse of the covariance matrix is called the precision matrix, denoted by Q = Σ − 1 {\displaystyle...
model that models the log-odds of an event as a linear combination of one or more independent variables. In regression analysis, logistic regression (or logit...
stochastic process Z(x) on a domain D, a covariance function C(x, y) gives the covarianceof the values of the random field at the two locations x and...
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar...
average value. It is the second central moment of a distribution, and the covarianceof the random variable with itself, and it is often represented by σ 2...
estimate the covariance or the spectrum of the process without assuming that the process has any particular structure. Methods of time series analysis may also...
(empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables...
"description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In...