What is the difference between ANOVA and ANCOVA?
ANOVA and ANCOVA are two statistical models used for equating samples or a group of one or more than one variables. They perform the same function but in a different way.
The main difference between ANOVA and ANCOVA is that ANOVA is a process of examining the difference among the means of multiple groups of data for homogeneity while ANCOVA is a technique that removes the impact of one or more metric-scaled undesirable variable from dependent variable before undertaking research.
The lesson provides the difference between ANOVA and ANCOVA with a comparison table for easier understanding between the two statistical techniques. Let’s find out:
Read More: Difference between One Way and Two Way ANOVA
What is ANOVA?
ANOVA is a statistical model used to observe the differences between the means of three or more variables in a population based on the sample presented.
It is a statistical technique commonly used in disciplines such as business, agriculture, economics, psychology, biology and education.
The core function of the statistical model is to check the presence of common mean among various groups.
The ANOVA is an abbreviation of Analysis of Variance and it is of two types as highlighted below:
- One way ANOVA is a method used when one variable is used to investigate the difference between different categories with many values.
- Two way ANOVA is a model where two factors are used simultaneously to investigate the interaction of the two factors influencing the values of a variable.
What is ANCOVA?
ANCOVA is an abbreviation of Analysis of Covariance. The statistical model has one or more variables with at least one continuous and one categorical predictor variable.
The method is regarded to be a midpoint between ANOVA and regression analysis. Here one variable in two or more variables can be compared.
The difference independent variables is as a result of the covariate being taken off by adjusting the dependent variable mean value within each treatment condition.
The core function of ANCOVA is testing the effect of outcome variable after removing the variance. Therefore, the statistical model is a linear relationship between dependent and independent variables.
Comparison Chart: ANOVA Vs ANCOVA
| Basic Terms | ANOVA | ANCOVA |
| Definition | It is tested to check the presence of common mean among various groups. | It is a test method for testing the effect of outcome variable after removing the variance. |
| Core Function | Used in both linear and non-linear model | Only used in a linear model |
| Includes | Categorical variable | Categorical and interval variable |
| Covariate | Ignored | Considered |
| BG variation | Attributes Between Group (BG) variation, to treatment. | Divides Between Group (BG) variation, into treatment and covariate. |
| WG variation | Attributes Within Group (WG) variation, to individual differences. | Divides Within Group (WG) variation, into individual differences and covariate. |
| Stands for | Analysis of Variance | Analysis of Covariance |
Core Difference between ANOVA and ANCOVA
- ANOVA ignore covariate while ANCOVA uses covariate
- The key feature of ANOVA is BG while ANCOVA BG is divided into TX and COV variation.
- ANCOVA uses linear model while ANOVA uses both linear and non-linear model
- ANCOVA comprises of both a categorical and a metric independent variable while ANOVA consist of a categorical independent variable only
- ANCOVA is more robust and unbiased unlike ANOVA
- ANCOVA WG variation is divided by individual differences as COV whereas ANOVA uses it for individual features only.
Comparison Video
https://youtu.be/p7fU02WRQ7Y
Summary
The core difference between ANOVA and ANCOVA is ANOVA uses both linear and non-linear model while ANCOVA strictly uses the linear model only. Understanding the two statistical techniques will make your assignment quite easy.
More Sources and References
- https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118491683
- https://towardsdatascience.com/doing-and-reporting-your-first-anova-and-ancova-in-r-1d820940f2ef
- https://www.slideshare.net/PrincyFrancisM/parametric-test-anova-ancova