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In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively. [1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval. [2]
Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature.
A categorical variable that can take on exactly two values is termed a binary variable or a dichotomous variable; an important special case is the Bernoulli variable. Categorical variables with more than two possible values are called polytomous variables; categorical variables are often assumed to be polytomous unless otherwise specified.
For example, the categorical variable(s) might describe treatment and the continuous variable(s) might be covariates (CV)'s, typically 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.
An example of conceptual moderation model with one categorical and one continuous independent variable. Cohen et al. (2003) recommended using the following to probe the simple effect of gender on the dependent variable ( Y ) at three levels of the continuous independent variable: high (one standard deviation above the mean), moderate (at the ...
This is a list of statistical procedures which can be used for the analysis of categorical data, also known as data on the nominal scale and as categorical variables. General tests [ edit ]
Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature.
Graphs that are appropriate for bivariate analysis depend on the type of variable. For two continuous variables, a scatterplot is a common graph. When one variable is categorical and the other continuous, a box plot is common and when both are categorical a mosaic plot is common. These graphs are part of descriptive statistics.