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When treating categorical variables such as ethnic groups and experimental treatments as independent variables in moderated regression, one needs to code the variables so that each code variable represents a specific setting of the categorical variable. There are three basic ways of coding: dummy-variable coding, contrast coding and effects coding.
Regression is a statistical technique used to help investigate how variation in one or more variables predicts or explains variation in another variable. Bivariate regression aims to identify the equation representing the optimal line that defines the relationship between two variables based on a particular data set.
The Burt table is the symmetric matrix of all two-way cross-tabulations between the categorical variables, and has an analogy to the covariance matrix of continuous variables. Analyzing the Burt table is a more natural generalization of simple correspondence analysis , and individuals or the means of groups of individuals can be added as ...
The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f.For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value.
The image above depicts a visual comparison between multivariate analysis of variance (MANOVA) and univariate analysis of variance (ANOVA). In MANOVA, researchers are examining the group differences of a singular independent variable across multiple outcome variables, whereas in an ANOVA, researchers are examining the group differences of sometimes multiple independent variables on a singular ...
The coefficient of multiple correlation is known as the square root of the coefficient of determination, but under the particular assumptions that an intercept is included and that the best possible linear predictors are used, whereas the coefficient of determination is defined for more general cases, including those of nonlinear prediction and those in which the predicted values have not been ...
Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potential to produce a "discovery". A stated confidence level generally applies only to each test considered individually, but often it is desirable to have a confidence level for the whole family of simultaneous tests. [4]
Group 1 is composed of two uncorrelated variables A and B. Group 2 is composed of two variables {C1, C2} identical to the same variable C uncorrelated with the first two. This example is not completely unrealistic. It is often necessary to simultaneously analyse multi-dimensional and (quite) one-dimensional groups.