Analysis of covariance

The analysis of covariance (English analysis of covariance, ANCOVA ) is a statistical method that combines analysis of variance and linear regression analysis. The goal is to hide the impact of a specific experiment relevant not (or not as relevant respected ) independent factors (so-called covariate or covariate ) on the dependent variable ( a noise reduction to match ), and so a possible effect of an interesting independent variable on to be able to statistically prove the dependent variable (increase in power).

Requirements

As with any statistical test some conditions the data must be fulfilled so that the generated test result is valid. When using the ANCOVA as provided in the use of ANOVA that the residuals are normally distributed and homoscedastic. In addition, a linear dependency of the dependent is provided by the independent variables analogous to linear regression.

Considerations for Power Analysis

Firstly, the statistical power for detecting a dependency is dependent on the / the independent variable (s ) is increased because a portion of the variance of the measured values ​​of the dependent variable is corrected by the parameter covariates. On the other hand, however, the number of degrees of freedom is reduced. When choosing a covariate with only a very small influence on the variance of the dependent variable, this reduces the statistical power of the test.

Some details

  • Typically covariates are taken into account in an experimental design to allow external influences less included in the dependent variable, thus reducing the variance of the measured values. Especially for small sample size, as well as well-chosen and well- measured covariates, the sensitivity of the statistical test can be improved.
  • The number of covariates should be kept as small as possible. Appreciated this number should be < (0.1 x sample size ) - be (number of groups -1).

Possible Problems

  • As with all statistical tests, the data must be checked before using the test if they fulfill the requirements for a correct test procedure at all.
  • With the definition of a covariate can not be corrected only a systematic (measurement) error of an experiment (bias ), but such a choice in a "wrong " variables are also introduced as a covariate. In clinical studies, it should refrain from this reason. Possible external " errors" that are reliably eliminated just by means of randomization, which is why this is the method of choice.
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