There are many statistical models in mathematics and different subjects. Different models are offered by the ANOVA and ANCOVA techniques. They have unique models and formulas for better solutions. Both are used in statistical and mathematical analysis. ANOVA is a test of means of groups ad ANCOVA is impacting on metric scales.

## ANOVA vs ANCOVA

**The main difference between ANOVA and ANCOVA is their process. The ANOVA is the process of examining groups for homogeneity. ANCOVA is the process of removing the impact on more than one metric scale. The ANOVA is using in both the linear and non-linear models. The ANCOVA is using only in the linear model. The attributes within Group(WG) in ANOVA vary with the individual. The divide within-group(DWG) varies from individual to many peoples.**

ANOVA stands for analysis of variance. The ANOVA is nothing but the estimated procedures of statistical analysis. Statistician Ronald Fisher is the one who found the ANOVA. In simple, It is the variation among groups. The main aim of ANOVA is to analyze the different means. The law of total variance is the concept of ANOVA, that is change in particular, and variance in components attributes. ANOVA is nothing but a statistical test to find the means of equality and differences.

ANCOVA stands for analysis of covariance. It is a general linear model in statistics. The main of ANCOVA is that the given thing of a dependent variable equals the independent variable. THE ANCOVA is also called treatment. The primary interest of ANCOVA is to controls the flow of continuous variables or covariates or nuisance variables. ANCOVA decomposes the variance in mathematics.

## Comparison Table Between ANOVA and ANCOVA

Parameters of comparison | ANOVA | ANCOVA |

Definition | ANOVA is a process of defining the means of groups | ANCOVA is the process of removing the impact on the metric scale. |

Models | ANOVA has both linear and non-linear models. | ANCOVA has only a linear model. |

Variables | ANOVA has only categorical variables. | ANCOVA has categorial and interval variables. |

Covariate | ANOVA ignores the covariate. | ANCOVA consider the covariate. |

BG variation | ANOVA has Attribute Between Group(BG) | ANCOVA has Divides Between Group(BG). |

WG variation | ANOVA has Attribute Within Group(WG). | ANCOVA has Divide Within Group(WG) |

## What is ANOVA?

In the 20th century, variance analysis have its fruition. the analysis includes hypothesis, partitioning, squares, etc. It also includes experimental techniques and models. In 1770, Laplace is the one who perform the hypothesis testing. The least-squares method was founded by Gauss and Laplace in 1800. After that, it is used in astronomy and geodesy. ANOVA is addressed using least square methods by Laplace in 1827. By using that, he measures the atmospheric tides.

In 1918, Ronald fisher is the one who found the term variance. ANOVA get popular with Ronald Fisher’s book called *Statistical Methods for Research Workers*. It was first published by Jerzy Neyman. The model has a linear relationship between the dependent variable and the independent variable. ANOVA is mainly used in complex relations for better solutions. The ANOVA has three different class models namely fixed-effect models, Random effect models, and mixed effect models.

The ANOVA is applied by several different approaches. The Linear model is the most basic used in ANOVA. The linear models only have perfect solutions, and the non-linear will cross the factor levels. The data will be balanced for better interpretation, and the unbalanced data need better understanding. The experimental units have the random assignment of treatments. Before the experiment, the randomization must be declared. The main aim of random assignment is for the null hypothesis.

## What is ANCOVA?

ANCOVA refers to the Analysis of covariance The ANCOVA can increase the capability of statistical power. By using this capability, it found the difference between groups by finding error variance within the group. The F-test is the basis for finding the differences. It is the concept of variance within the different groups. ANCOVA also adjusts the preexisting differences within the groups.

The main controversial concept in ANCOVA is for correcting the differences that exist within the DV. But in these circumstances, it is impossible to equal by random assignments. CV is used for adjusting the values in ANCOVA. But these covariates didn’t find statistical techniques and can’t equate the groups. The IV removing the variance intimated by CV is always associated with DV and also removes the considerable variable from the groups that result in meaningless solutions.

ANOVA is fundamentally used in comparative analysis. It finds different outcomes of interest. The ratio of two variances can determine the statistical significance. But the ratio is independent of the observations. The significance does not alter by adding the constants and multiplying the constants. The units are using the expressing observations for solutions. To simplify the data we always subtract the constant from the values. Data coding is a good example of ANCOVA.

## Main Differences Between ANOVA and ANCOVA

- ANOVA is a process of defining the means of groups, and ANCOVA is the process of removing the impact on the metric scale.
- ANOVA has both linear and non-linear models, and ANCOVA has only a linear model.
- ANOVA has only categorical variables., and ANCOVA has categorical and interval variables.
- ANOVA ignores the covariate., and ANCOVA considers the covariate.
- ANOVA has Attribute Between Group(BG), and ANCOVA has Divides Between Group(BG).

## Conclusion

Both the ANOVA and ANCOVA have a unique technique for statistical analysis. ANOVA can work on both linear and non-linear models. ANCOVA only works with linear models. Both have several techniques and models for better solutions. The formulas will help to find the results easily. The more complex algorithms are done by ANOVA. Many types of analysis methods are available in the ANOVA technique. The ANCOVA technique has several assumptions methods. The ANCOVA also considers the power techniques helpful for mathematical analysis.

## References

- https://books.google.com/books?hl=en&lr=&id=T6uvhsy8d_8C&oi=fnd&pg=PP1&dq=anova+and+ancova&ots=Kl1Uv1Eh8G&sig=cTJzzdRgrCWQvBW-BifjYxiVcBY
- https://books.google.com/books?hl=en&lr=&id=ZVX7Un6GGysC&oi=fnd&pg=PA77&dq=anova+and+ancova&ots=OvlmAGy8x7&sig=KRh8RfaR1eJY-XlML2zLQGTyG-U

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