# Analysis of covariance (ANCOVA)

Quantitative Results
Statistical Analysis

Analysis of covariance (ANCOVA) is used in examining the differences in the mean values of the dependent variables that are related to the effect of the controlled independent variables while taking into account the influence of the uncontrolled independent variables.

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Analysis of covariance (ANCOVA) can be used to determine the variation in the intention of the consumer to buy a particular brand with respect to different levels of price and the consumer’s attitude towards that brand.

Analysis of covariance (ANCOVA) can be used to determine how a change in the price level of a particular commodity will affect the consumption of that commodity by the consumers.

Analysis of covariance (ANCOVA) consists of at least one categorical independent variable and at least one interval natured independent variable. In Analysis of covariance (ANCOVA), the categorical independent variable is termed as a factor, whereas the interval natured independent variable is termed as a covariate. The task of the covariate in Analysis of covariance (ANCOVA) is to remove the extraneous variation from the dependent variable. This is done because the effects of the factors are of major concern in Analysis of covariance (ANCOVA).
Analysis of covariance (ANCOVA) is most useful in those cases where the covariate is linearly related to the dependent variables and is not related to the factors.

Similar to Analysis of variance (ANOVA), Analysis of covariance (ANCOVA) also assumes similar assumptions. The following are the assumptions of Analysis of Covariance (ANCOVA):
The variance in Analysis of covariance (ANCOVA) that is being analyzed must be independent.
In the case of more than one independent variable, the variance in Analysis of covariance (ANCOVA) must be homogeneous in nature within each cell that is formed by the categorical independent variables.

The data should be drawn from the population by means of random sampling in Analysis of covariance (ANCOVA). Analysis of covariance (ANCOVA) assumes that the adjusted treatment means those that are being computed or estimated are based on the fact that the variables obtained due to the interaction of covariate are negligible.

The Analysis of covariance (ANCOVA) is done by using linear regression. This means that Analysis of covariance (ANCOVA) assumes that the relationship between the independent variable and the dependent variable must be linear in nature.

In Analysis of covariance (ANCOVA), the different types of the independent variables are assumed to be drawn from the normal population having a mean of zero.

The Analysis of covariance (ANCOVA) assumes that the regression coefficients in every group of the independent variable must be homogeneous in nature.

Analysis of covariance (ANCOVA) is applied when an independent variable has a powerful correlation with the dependent variable. But, it is important to remember that the independent variables in Analysis of covariance (ANCOVA) do not interact with other independent variables while predicting the value of the dependent variable. Analysis of covariance (ANCOVA) is generally applied to balance the effect of comparatively more powerful non interacting variables. It is necessary to balance the effect of interaction in Analysis of covariance (ANCOVA) in order to avoid uncertainty among the independent variables.

Analysis of covariance (ANCOVA) is applied only in those cases where the balanced independent variable is measured on a continuous scale.

Let us assume a researcher wants to determine the effect of an in-store promotion on sales revenue. In this case, Analysis of covariance (ANCOVA) is an appropriate technique because the change in the attitude of the consumer towards the store will automatically affect the sales revenue of the store in Analysis of covariance (ANCOVA). Therefore, in Analysis of covariance (ANCOVA), the dependent variable will be the sales revenue of the store. And the independent variable will be the attitude of the consumer in Analysis of covariance (ANCOVA).