Statistics How To

Nuisance Variable & Nuisance Parameter: Definition, Examples

Types of Variables > Nuisance Variable

What is a Nuisance Variable?

nuisance variable

Nuisance variables increase the variability in an experiment.

A nuisance variable is a type of extraneous variable that causes an increase in variability within groups in an experiment. These variables tend not to differ between levels of an independent variable (like confounding variable), but they increase variability of the scores overall.


Example: A researcher is investigating how easy it is to lose weight. Potential nuisance variables include:

  • Ease of weight loss is probably related to how much a person is overweight.
  • Some people might have a genetic predisposition to be overweight.

Nuisance Factor

A related term is a nuisance factor — a factor in blocking that has an effect on the response variable but is of no interest to the research topic. If a nuisance factor is known but uncontrollable, you may be able to use ANCOVA to estimate the factor’s effect and remove it from your results. If a nuisance factor is unknown and uncontrollable, randomization can mitigate its effect.

Nuisance Parameter

The terms “nuisance variable” and “nuisance parameter” are sometimes used interchangeably. In Bayesian analysis, they are essentially equal. In frequentist statistics, they are they slightly different. Both are unwanted in an analysis or experiment. But while a nuisance variable is a random variable, a nuisance parameter is a population parameter. For example, the population variance, σ2 is a nuisance parameter for a normal distribution when the population mean, μ, is the parameter of interest.

Ways to minimize nuisance variables

Obviously the easiest way to deal with these variables is to find out what they are and remove them from the experiment. In most cases, that’s just not possible as they tend to be intrinsic to the experiment (like the weight loss example above). However, there are several ways you can minimize their effect:

  • Blocking: if your variable is known and controllable, you can add it to your experimental design as another independent variable.
  • Statistical control: if your variable is known but not controllable by blocking, use ANCOVA or partial correlation to hold the unwanted variable constant.
  • Randomization: if you don’t know what your nuisance variable is, randomization can balance out the effect of any potentials. This technique can also be used after you’ve used blocking on the most important variables and want to reduce the effects of the remaining known or unknown variables.
  • Latin Square Design: if you have two nuisance variables, this experimental design can isolate them. The levels of one are assigned to the rows and the levels of the other are assigned to the columns.

References:
Basu, D. (1977), “On the Elimination of Nuisance Parameters,” Journal of the American Statistical Association, vol. 77, pp. 355–366. doi:10.1080/01621459.1977.10481002
Irving B. Weiner, John A. Schinka, Wayne F. Velicer. Handbook of Psychology, Research Methods in Psychology. Available here.

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Nuisance Variable & Nuisance Parameter: Definition, Examples was last modified: October 12th, 2017 by Stephanie Glen