# Analysis of Covariance (Statistics)

The blue area is subdivided again: into the real error and into a part explained by covariates.

The analysis of covariance ( English analysis of covariance , shortly ANCOVA ), rarely Mitstreuungszerlegung is ,, a statistical method that analysis of variance  (ANOVA) and linear regression analysis combines.

The aim is to determine the effect of covariates or covariates, i. H. of uninteresting independent variables to fade out to the dependent variable (reduction of the noise ) and thus to be able to statistically prove a possible effect of an interesting independent variable on the dependent variable (increase of the discriminatory power ).

## requirements

As with any statistical test , when using the ANCOVA, certain data requirements must be met in order for the test result to be valid :

## Considerations for the analysis of the selectivity

On the one hand, the selectivity is a test for the detection of a dependency of the dependent / independent variable (s) by the covariance increases , as a part of the variance is corrected to the measured values of the dependent variable with the covariate.

On the other hand, however, the number of degrees of freedom is reduced. Choosing a covariate with only very little influence on the variance of the dependent variable reduces the discriminatory power of the test.

## Some details

• Typically, covariables are taken into account in an experimental design in order to reduce the influence of external influences on the dependent variable and thus to reduce the variance of the measured values. The sensitivity of the statistical test can be improved, especially with a small sample size and well-selected and well-measured covariates .
• The number of covariates should be kept as small as possible. Estimated it should be <(0.1 x sample size) - (number of groups - 1).

## Possible problems

• As with all statistical tests, the data must be checked before the test is used to determine whether it meets the requirements for a correct test execution.
• With the definition of a covariate, not only can a systematic (measurement) error of an experiment ( bias ) be corrected, but one can also be introduced as a covariate if a “wrong” variable is selected.
• In the context of clinical trials should dispense with analysis of covariance for this reason. Instead, possible external “errors” can be reliably eliminated by randomization .
• The analysis of covariance (like all statistical methods) should not be a last resort to “force” a significant statement after the experiment . If one has to start from a covariate, then this should be defined during the design of the experiment and recorded in the protocol.

## literature

• Bortz, J. & Schuster, C. (2010). Analysis of Covariance. In: Statistics for human and social scientists . 7th edition (pp. 305-323). Berlin and Heidelberg: Springer, ISBN 978-3-642-12769-4 .
• Olejnik, SF & Algina, J. (1985). A Review of Nonparametric Alternatives To Analysis of Covariance. Evaluation Review, 9 (1) , 51-83, doi : 10.1177 / 0193841X8500900104 .

## Individual evidence

1. ^ Arthur Linder: Statistical methods: For natural scientists, physicians and engineers p. 220