Variables other than independent, dependent, and nuisance sometimes become important in the experiment. A control variable is essentially a nuisance variable that is held fixed through the selection of subjects or experimental trials. For example, the variance may be held low by controlling the subject selection so that only males between the ages of 18 and 21 are used in the experiment. The approach helps to improve the confidence in the conclusions from the experiment, possibly with a smaller number of subjects or trials, but might prevent its findings from being generalized to settings outside of the control.
A confounding variable is an extraneous variable that causes the independent and dependent variables to be correlated, but they become uncorrelated once the value of the confounding variable is given. For example, having a larger shoe size may correlate to better speaking ability. In this case the confounding variable is the person's age. Once the age is known, we realize that older people have larger feet then small children, and are also better at speaking. This illustrates the danger of inferring causal relationships from statistical correlations.
Steven M LaValle 2020-01-06