ANCOVA Assumptions

ANCOVA Assumptions

In statistics, analysis of covariance (ANCOVA) is a general linear model with a continuous outcome variable (quantitative, scaled) and two or more predictor variables where at least one is continuous (quantitative, scaled) and at least one is categorical (nominal, non-scaled). ANCOVA is a merger of ANOVA and regression for continuous variables. ANCOVA tests whether certain factors have an effect on the outcome variable after removing the variance for which quantitative predictors (covariates) account. The inclusion of covariates can increase statistical power because it accounts for some of the variability.

Like any statistical procedure, the interpretation of ANCOVA depends on certain assumptions about the data entered into the model. For instance, the F-test assumes that the errors are normally distributed and homoscedastic. Since ANCOVA is a method based on linear regression, the relationship of the dependent variable to he independent variable(s) must be linear in the parameters.Simplifying assumption (not necessary to run ANCOVA): homogeneity of regression which says that the relationship between the covariate and the dependent variable should be similar across all groups of the independent variable.

In ANCOVA, assumptions include at least one categorical independent variable and at least one interval or metric independent variable. The categorical independent variable is called a factor, whereas the metric independent variable is called a covariate.

In ANCOVA assumptions, the most common use of covariate is to remove extraneous variations from the dependent variable. This is because in ANCOVA assumptions, the effect of factors is of major concern.

Like ANOVA, ANCOVA assumptions have similar assumptions. These assumptions are as follows:

The variance that is being analyzed or estimated should be independent, which also holds true for ANCOVA assumptions.

In ANOVA, the variable which is dependent in nature must have the same variance in each category of the independent variable. In the case of more than one independent variable, the variance must be homogeneous in nature, within each cells formed by the independent categorical variables, which also holds true for ANCOVA assumptions.

In ANOVA, it is assumed that the data upon which the significance test is conducted is obtained by random sampling, which also holds true for ANCOVA assumptions.

When analysis of variance is conducted on two or more factors, interactions can arise. An interaction occurs when the effect of independent variables on a dependent variable is different for different categories, or levels of another independent variable. If the interaction is significant, then the interaction may be ordinal or disordinal. Disordinal interaction may be of a no crossover or crossover type. In the case of the balanced designs, while conducting ANCOVA assumptions, the relative importance of factors in explaining the variation in the dependent variable is measured by omega squared. Multiple comparisons in the form of a priori or a posteriori contrast can be used for examining differences among specific means in ANCOVA assumptions.

In ANCOVA assumptions, the adjusted treatment means the computed or the estimated are based on the fact that the variable by covariate interaction is negligible. If this ANCOVA assumption is violated, then the adjustment of the response variable to a common value of the covariate will be misleading.So in ANCOVA assumptions, the relationship between the independent and dependent variable must be linear in the parameters. Thus, in ANCOVA assumptions, the different levels of the independent variable will follow normal distribution with mean zero. ANCOVA assumptions combine with the assumption of linear regression. The method of ANCOVA assumptions is done by using a linear regression.

ANCOVA assumptions also assume the homogeneity of regression coefficients which is based on the fact that the regression coefficient for every group present in the data of the independent variable should be same. If this fact of ANCOVA assumptions is violated, then the ANCOVA assumption will be misleading.