Dependent and independent variables
In
mathematics, an independent variable is any of the
arguments, i.e. "inputs", to a
function. These are contrasted with the dependent variable, which is the value, i.e. the "output", of the function. Thus if we have a function f(x), then x is an independent variable, and f(x) is a dependent variable. The dependent variable depends on the independent variables; hence the names.
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Dependent Variables
the variables in a research experiment which are affected by manipulation of the explanatory or experimental variables. See
Experimental Variables.
Independent vs. Dependent Variables
The terms dependent and independent variable apply mostly to experimental research where some variables are manipulated, and in this sense they are "independent" from the initial reaction patterns, features, intentions, etc. of the subjects. Some other variables are expected to be "dependent" on the manipulation or experimental conditions. That is to say, they depend on "what the subject will do" in response. Independent variables are those that are manipulated whereas dependent variables are only measured or registered.
Somewhat contrary to the nature of this distinction, these terms are also used in studies where we do not literally manipulate independent variables, but only assign subjects to "experimental groups" based on some preexisting properties of the subjects. For example, if in an experiment, males are compared with females regarding their white cell count (WCC), Gender could be called the independent variable and WCC the dependent variable.
See
Dependent vs. independent variables for more information.