Difference Between ANCOVA and ANOVA (With Table)

Statistical models are the combination of different conjectures that have been made by collecting data and predicting information based on it. They play a crucial role in something as simple as a person’s daily life. ANCOVA and ANOVA are two statistical models that are used by analysts and mathematicians worldwide.

ANCOVA vs ANOVA

The difference between ANCOVA and ANOVA is that ANCOVA is the process of eliminating the impact of metric-scaled variables from dependent variables before carrying out a research project. Meanwhile, ANOVA is a method used for investigating the difference among the means of various groups of data for the purpose of uniformity.

ANCOVA is short for ‘Analysis of Covariance’. The reason for using this method is to evaluate if the means of a dependent variable are uniform across the levels of categorical independent variables. This is done while controlling the effects that non-important continuous variables have. This type of model is functional in general linear models.

ANOVA is short for ‘Analysis of Variance’. This is an analysis tool that provides a technique to examine and analyze the difference between the means of various groups of data. In simple terms, it is a method to find out whether the results of a survey or experiment are noteworthy. This type of model can be functional in linear as well as non-linear models. 

Comparison Table Between ANCOVA and ANOVA

Parameters of ComparisonANCOVAANOVA
MeaningANCOVA evaluates the existence of a uniform mean across various groups of variables.ANOVA analyzes the difference between means of various groups of data.
AbbreviationANCOVA is short for ‘Analysis of Covariance’.ANOVA is short for ‘Analysis of Variance’.
FunctionsANCOVA is used only in general linear models.ANOVA is used in linear as well as non-linear models.
InclusionsANCOVA includes categorical as well as interval variables.ANOVA only includes categorical variables.
CovariateThe covariate is always considered in the case of using ANCOVA.The covariate is not considered in the case of using ANOVA.
NatureANCOVA is more robust as compared to the latter.ANOVA is not as robust and has chances of being biased.
WG VariationANCOVA splits WG variation into covariate and individual differences.ANOVA assigns WG variation to individual differences.
BG VariationANCOVA splits BG variation into covariate and treatment.ANOVA assigns BG variation to treatment.

What is ANCOVA?

ANCOVA, or analysis of covariance, is a technique of examining if the means of dependent variables are uniform across the levels of categorical independent variables. These independent variables are also called ‘treatment’. Moreover, it controls the effects of other continuous variables that are not as important. These variables are also called ‘Covariates’.

ANCOVA is used for only general linear models. This type of model blends analysis of variation with regression. The model can function as a method to increase the statistical power by lowering the error variance that lies within the groups. Moreover, it can even calibrate for differences that already exist in groups that are intact.

While using ANCOVA, there are 5 basic assumptions that are made. These include linearity of regression, homogeneity of error variances, independence of error terms, normality of error terms, and homogeneity of regression slopes. These assumptions also affect the interpretation of the results. Moreover, it is further assumed that the slope of the covariates is equal across all groups containing treatments.

When examining the results, there is an important main effect if there is a noteworthy difference between the levels of one independent variable. This is when all the other factors are ignored.

What is ANOVA?

ANOVA, or analysis of variance, is a method that is used to evaluate the difference between the means of various groups of data. It is a statistical tool that splits an observed aggregate variability that can be seen inside a data. This data is often set into two parts – random factors and systematic factors.

In simple terms, ANOVA is the first step towards analysing the results that various factors have on a given set of data. On finishing the test or research, an analyst carries out more tests on the factors that give in to the inconsistency of the set of data. The ANOVA test results are used in an f-test for creating additional data that readjust with the proposed regression models.

Another function of ANOVA is to compare two or more groups at once with the purpose of determining if they have a relationship. The outcome of the formula paves a way to analyse various data groups to determine the variability that exists within or between samples. If no difference is found, it is called a null hypothesis.

ANOVA is of two main types – one way and two ways. These depend on the number of variables that exist in the outcome of a variance test.

Main Differences Between ANCOVA and ANOVA

  1. ANCOVA evaluates the existence of a uniform mean across various groups of variables while ANOVA analyzes the difference between means of various groups of data.
  2. ANCOVA is short for ‘Analysis of Covariance’ while ANOVA is short for ‘Analysis of Variance’.
  3. ANCOVA is used only in general linear models while ANOVA is used in linear as well as non-linear models.
  4. ANCOVA includes categorical as well as interval variables whereas ANOVA only includes categorical variables.
  5. ANCOVA always considers the covariate while ANOVA ignores it.
  6. ANCOVA is more vigorous and unbiased as compares to ANOVA.

Conclusion

ANCOVA and ANOVA are two terms that are very common in the world of statistics. These are statistical models that have a similar name but different concepts. A major distinguishing feature among the two is that ANCOVA only functions in general linear models while ANOVA functions in linear as well as non-linear models.

Moreover, ANCOVA is considered to be the stronger and more vigorous method as compared to ANOVA. This is because ANCOVA is relatively unbiased. Another way to determine the difference between ANCOVA and ANOVA is to understand how ANCOVA always uses a covariate while ANOVA always ignores it.

References

  1. https://books.google.com/books?hl=en&lr=&id=ZVX7Un6GGysC&oi=fnd&pg=PA77&dq=anova+vs+ancova&ots=OvllvDAdD2&sig=L8Mein9MUAIkQhGEZ4r8jDFiWoU
  2. https://journals.sagepub.com/doi/abs/10.3102/00346543068003350
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