covariate

Examples of covariate in the following topics:

• Additional Properties of the Binomial Distribution

  • In this section, we'll look at the median, mode, and covariance of the binomial distribution.
  • If two binomially distributed random variables X and Y are observed together, estimating their covariance can be useful.
  • Using the definition of covariance, in the case n = 1 (thus being Bernoulli trials) we have .

• Models with Both Quantitative and Qualitative Variables

  • A regression model that contains a mixture of quantitative and qualitative variables is called an Analysis of Covariance (ANCOVA) model.
  • They are the statistic control for the effects of quantitative explanatory variables (also called covariates or control variables).
  • Covariance is a measure of how much two variables change together and how strong the relationship is between them.
  • Analysis of covariance (ANCOVA) is a general linear model which blends ANOVA and regression.
  • However, even with the use of covariates, there are no statistical techniques that can equate unequal groups.

• Two Regression Lines

  • ANCOVA can be used to compare regression lines by testing the effect of a categorial value on a dependent variable, controlling the continuous covariate.
  • A method known as analysis of covariance (ANCOVA) can be used to compare two, or more, regression lines by testing the effect of a categorial value on a dependent variable while controlling for the effect of a continuous covariate.
  • Covariance is a measure of how much two variables change together and how strong the relationship is between them.
  • Analysis of covariance (ANCOVA) is a general linear model which blends ANOVA and regression.
  • ANCOVA evaluates whether population means of a dependent variable (DV) are equal across levels of a categorical independent variable (IV), while statistically controlling for the effects of other continuous variables that are not of primary interest, known as covariates (CV).

• Multivariate Testing

  • Because measures of this type are usually highly correlated, it is not advisable to conduct separate univariate $t$-tests to test hypotheses, as these would neglect the covariance among measures and inflate the chance of falsely rejecting at least one hypothesis (type I error).
  • where $n$ is the sample size, $\bar { x }$ is the vector of column means and $S$ is a $m \times m$ sample covariance matrix.

• Making Inferences About the Slope

  • Specifically, the interpretation of $m$ is the expected change in $y$ for a one-unit change in $x$ when the other covariates are held fixed—that is, the expected value of the partial derivative of $y$ with respect to $x$.
  • This may imply that some other covariate captures all the information in $x$, so that once that variable is in the model, there is no contribution of $x$ to the variation in $y$.
  • This would happen if the other covariates explained a great deal of the variation of $y$, but they mainly explain said variation in a way that is complementary to what is captured by $x$.

• Comparing Nested Models

  • Furthermore, multilevel models can be used as an alternative to analysis of covariance (ANCOVA), where scores on the dependent variable are adjusted for covariates (i.e., individual differences) before testing treatment differences.

• Using the Model for Estimation and Prediction

  • This could happen because the covariance that the first independent variable shares with the dependent variable could overlap with the covariance that is shared between the second independent variable and the dependent variable.

• The Role of the Model

  • Furthermore, one may assume that the mean response level in the population depends in a truly linear manner on some covariate (a parametric assumption), but not make any parametric assumption describing the variance around that mean.

• Coefficient of Correlation

  • Pearson's correlation coefficient between two variables is defined as the covariance of the two variables divided by the product of their standard deviations.