Table of Contents

## 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 affects 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 that it considers 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 considered.

## Difference Between ANOVA and ANCOVA

- 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.
- ANOVA doesn’t take into account the covariate. Whereas, ANCOVA includes covariate.
- 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.
- ANOVA does not eliminate the effect of unwanted factors but, ANCOVA removes the impact of unwanted factors.
- ANOVA has both linear and non-linear models, whereas ANCOVA has only one model, namely, linear.

## Comparison Between ANOVA and ANCOVA

Parameters of Comparison | ANOVA | ANCOVA |

Definition | The 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 variables | One or two | Two or more than two |

Covariate | Not present | Present |

Model | Can be linear or non-linear | Linear |

Purpose | Comparing multiple groups at a time. | Comparing one independent variable at a time.It eliminates the effect of unwanted elements(covariate). |

Measures | Experimental effects and errors. | Effects Errors Covariate. |