Difference Between ANOVA and ANCOVA (With Table)

Statistics is the backbone of research work. Almost all hypotheses rely on quantitative analysis. There are several ways to establish relationships or create contrasts between entities. Depending on your needs, you can choose the appropriate method from the long list available. Out of hese two methods are ANOVA and ANCOVA.

ANOVA vs ANCOVA

The main difference between ANOVA and ANCOVA is that ANOVA stands for Analysis of Variance, used to compare two or more groups of independent variables. ANCOVA, on the other hand, is an acronym for “analysis of covariance”. It is an improved version of ANOVA. It has an additional factor called covariate.

Analysis of variance (ANOVA) is a statistical method with one dependent variable and one independent variable. The independent variable is further divided into more than two groups. There are two subcategories: one-way ANOVA and two-way ANOVA. Statistical comparisons and contrasts of variables or means help to reject or revise hypotheses.

ANCOVA, or Analysis of Covariance, is one step ahead of ANOVA. There are two or more independent variables, one dependent variable, and a covariate. It i it controls the linear influence of a variable that affects the outcome. Its main purpose is to control the effects of concomitant species.

Comparison Table Between ANOVA and ANCOVA

Parameters of ComparisonANOVAANCOVA
DefinitionThe method used to compare two or more groups of IVs( independent Variables) and analyze hypotheses.It is an advanced version of ANOVA that is helpful when a covariate exists.
Number of independent variablesOne or twoTwo or more than two
CovariateNot presentPresent
ModelCan be linear or non-linearLinear
PurposeComparing multiple groups at a time.Comparing one independent variable at a time.It eliminates the effect of unwanted elements(covariate).
MeasuresExperimental effects and
errors.
Effects
Errors
Covariate.

What is ANOVA?

ANOVA is also termed as “the fisher analysis of variance “. It was brought into existence by Ronald Fisher. It is a short form of analysis of variance. Furthermore, it has a single dependent and independent variable. The independent variable has further divisions( more than 2).

It can function as both a linear and nonlinear model. It is used only for differentiating purposes. It is used in both maths and research. It is used to test the significance of the difference between more than 2 sample means and make interference.

It is divided into two types, namely, one-way and two-way ANOVA. One-way ANOVA is used when one independent variable has more than two groups. If two groups are present in one independent variable, then a t-test is a better choice.

Two-way ANOVA is helpful when two independent variables are present. This variable has further subdivisions (more than 2 for each).

An example of ANOVA is the number of sitting hours for studying. It can be divided into three groups, namely, high, mediocre and low and see how it is affecting academic grades.

For two-way ANOVA, consider the example of the number of sitting hours and mobile phone use. Then, its effect is seen on academic grades. Here, there are two independent variables and one dependent variable.

What is ANCOVA?

The addition of just a “C” adds up a whole lot to ANOVA and makes it ANCOVA. It can be understood as the combination of ANOVA and regression. It can have multiple independent variables. In simplest cases, at least one independent, dependent variable and a covariate should be present.

It is easy to differentiate it from ANOVA and memorize, as it has an additional “C” .This “C” stands for covariance. This method is used to eliminate the effect of covariance on the results. It has 3 components i.e. errors, effects, covariate.

It is useful when a linear relationship exists between the dependent variable and the ancillary variate(covariate). Even ANCOVA can be labelled as one-way and two-way ANCOVA. It is an upgraded version of ANOVA in the sense that it takes into account the non-primary elements for margin of error in the result.

An example of one-way ANCOVA is the effect of medication on recovery time from surgery, where the number of hours a person rests is the covariate. It will affect the outcome. The more the person rests, the less time he/ she takes to recover. If a person pushes his/ her limits and exhausts the body, it will take more time for recovery.

Similarly, in two-way ANCOVA, two independent variables like medication and a balanced diet can be taken into consideration.

Main Differences Between ANOVA and ANCOVA

  1. ANOVA is a method used to differentiate between means or to check the hypothesis. On the contrary hand, ANCOVA evaluates the relationship between independent and dependent variables taking into account other unimportant variables.
  2. ANOVA doesn’t take into account the covariate. Whereas, ANCOVA includes covariate.
  3. In ANOVA, minimum two variables i.e. dependent and independent variables required. In ANCOVA, a minimum of three variables i.e. dependent, independent variables, and covariate.
  4. ANOVA does not eliminate the effect of unwanted factors but, ANCOVA removes the impact of unwanted factors.
  5. ANOVA has both linear and non-linear models, whereas ANCOVA has only one model, namely, linear.

Conclusion

Both the terms ANOVA and ANCOVA are used to describe methods used in stats and research work to evaluate differences. They are closely related. ANOVA is used when an independent variable has more than 2 groups. It can also be used to differentiate between groups of 3 or more means.

ANCOVA or analysis of covariance is an upgraded version of ANOVA. It is used in the presence of covariates. These covariates are factors that are not of primary importance in the result but ultimately affect it. ANCOVA helps in controlling the impact of the extraneous variable. It has a wider scope than ANOVA.

References

  1. https://www.tandfonline.com/doi/abs/10.1080/03610919808813500
  2. https://journals.sagepub.com/doi/abs/10.3102/1076998613509405