Difference Between ANOVA and ANOCVA (With Table)

ANOVA vs ANOCVA

The key difference between ANOVA and ANOCVA is that ANOVA (Analysis of Variance) studies the variance of the statistical data for analysis and ANOCVA (Analysis of Covariance) studies the covariance of the statistical data for analysis.

ANOVA and ANOCVA are two different techniques used in statistics for analyzing the given data or sample either with one variable or more than one variable.

That is if we are using ANOVA, we need to know the variance of the data or sample and on the other hand, if we are using ANOCVA we need to know the covariance of the statistical data.

The choice of technique depends on the data which is being studied i.e. it depends on the category and nature of data.


 

Comparison Table Between ANOVA and ANOCVA (in Tabular Form)

Parameter of ComparisonANOVAANOCVA
MeaningANOVA examines the variance of the given statistical data.ANOCVA examines the covariance of the data for analysis.
Use of covarianceANOVA doesn’t use Covariance.ANOCVA uses Covariance.
ReliableLess reliable as compared to ANOCVA.ANOCVA is more reliable and unbiased compared to ANOVA.
ModelANOVA uses linear as well as non-linear models.Whereas ANOCVA uses only a general linear model.
VariableANOVA includes categorical variables.ANOCVA includes categorical as well as interval variables.

 

What is ANOVA?

ANOVA stands for ‘Analysis of Variance’. It is a statistical technique used for the analysis of a given sample or data having one or more than one variable.

It is used to observe the difference between the means of two or three or more variables present in a sample.

It can be used for the linear model as well as the non-linear model. ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means.

To use the ANOVA model, we simply divide the variations within the group into the treatments.

It is a widely used technique and also a popular method as it includes less work and quick results can be calculated by using ANOVA. Also, the chances of error are less.  

It is generally used in sectors like agriculture, psychology, etc. it has various models and types.

Let’s take a look at various types and models of ANOVA.

Types of ANOVA-:

  1.  One-way ANOVA– it is used to test the differences between two or more independent groups of data.
  2. Factorial ANOVA– it is used for the study of the interaction effects among treatments (levels of a categorical independent variable).
  3. Repeated measures ANOVA– This type of ANOVA is used when the same subject is used for each treatment.
  4. Multivariate analysis of variance– Commonly known as MANOVA, it is used when there is more than one response variable.

Classes of ANOVA Models-:

  1. Fixed-effects models.
  2. Random- effect models.
  3. Mixed-effect models.
Demonstration of ANOVA
Demonstration of ANOVA
 

What is ANOCVA?

ANOCVA stands for ‘Analysis of Covariance’. It is also a statistical tool used for the analysis of a sample or group of samples of one or more than one variable based on the Covariance.

It uses the general linear model i.e. it implies that the dependent variable and independent variable have a linear relationship.

It is more reliable as it uses covariance which makes it statistically more powerful. ANOCVA is difficult to calculate as compared to ANOVA.

We can understand it as ANOVA and regression used together to some extent i.e. the two variables (dependent and independent) are related to each other in a linear relation. Also, they have a homogeneity that comes due to the regression.

Further, the use of ANOCVA and results obtained from it depends completely on the type and nature of data.

Generally, ANOCVA checks whether different means of the sample that have been adjusted for differences in independent variables differ on the different levels of dependent variables.

In short, ANOCVA is actually an ANOVA model.

Calculation of ANOCVA
Calculation of ANOCVA

Main Differences Between ANOVA and ANOCVA

  1. ANOVA uses both linear and non-linear models. While ANOCVA only uses a general linear model.
  2. We need to find co-variance for using ANOCVA. But in the case of ANOVA covariance is of no use.
  3. ANOVA is a statistical technique used to observe the difference between the variables. On the other hand, ANOCVA is a model of ANOVA.
  4. ANOCVA is unbiased and more reliable as compared to ANOVA.
  5. Due to the use of covariance ANOCVA is more statistically powerful as compared to ANOVA which does not use covariance.
  6. ANOVA divides within-group variations to treatments. While ANOCVA divides the between-group variations into treatment and covariate.
  7. ANOCVA is a more advanced way of studying the data as compared to ANOVA.
  8. ANOCVA combines both ANOVA and regression. Therefore more preferable than ANOVA.
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Frequently Asked Questions (FAQ) About ANOVA and ANOCVA

Is a two way ANOVA a factorial ANOVA?

A two-way ANOVA is generally not a factorial Anova. The major difference between both of them is:

  1. Two-way ANOVA – A two-way ANOVA helps us understand whether there is an interaction between the two independent variables. It simply adds one independent variable to the regression.
  2. Actorial ANOVA – On the other hand, a factorial variable is used to determine the mean of two or more independent variables. It simply adds one, two or more numbers of independent variables to the regression.

🔥 What are the assumptions of ANOVA?

The assumptions of Anova are:

  1. Normal distribution of dependant variable in each group
  2. Equal variance for the population in each group
  3. Independently drawn samples
  4. Observations are independent and random in each sample
  5. Additive factor effects

🍋 Is ANOVA Parametric?

ANOVA is parametric but it can also be non-parametric. When it is used for score data it becomes parametric and when it is used for ranking or order data, it becomes non-parametric.

🍌 What does the P-value mean in ANOVA?

P-value represents the probability of observing a result in a statistical hypothesis test at least as extreme as an actually observed result.

🍉 What is the null hypothesis for ANOVA?

There are different null hypotheses for one and two way Anova.
The null hypothesis for one way ANOVA – mean of dependant variable for all groups will be same

The null hypothesis for two way ANOVA – three different null hypothesis as listed below:

  1. Means are the same for the same factor group observations
  2. Means are the same for the observations grouped by different factors
  3. Two factors do not interact

🍎 What is the difference between Anova and t-test?

Both t-test and ANOVA are used to determine the differences in the population means of different groups.

The major difference between Anova and t-test is that t-test is used to examine the difference in the mean of two groups only.

On the other hand, ANOVA is similar to running multiple t-tests. It can examine more than two groups.


 

Infographic

ANOVA vs ANOCVA

 

Learn More With the Help of Video


 

Conclusion

Both the techniques (ANOVA and ANOCVA) are for analyzing the statistical data or sample having one or more than one variable. Where ANOVA uses only the variance, ANOCVA uses the covariance to find out the results.

ANOVA uses both linear and non-linear models for study. On the other hand, ANOCVA only uses the general linear model for the study. As compared to ANOVA, ANOCVA is more reliable and unbiased.

ANOVA has less calculation work as compared to ANOCVA, as in ANOCVA first, we have to divide the variations in treatment and covariate and then we need to calculate the covariance.

ANOCVA is a model of ANOVA and it includes both ANOVA and regression.

Though ANOCVA is a statistically more powerful technique as it uses covariance and also combines ANOCVA and regression, we cannot use it every time.

The choice of the best technique for analysis and concluding depends on the nature and type of data. Statistics can only give us results, interpreting the results depends on people using it.

That is there are various techniques in statistics for the same purpose and all of them give different-different results. Therefore, choosing the right technique is most important to get the correct and most helpful results.

Similarly, we cannot conclude that the use of ANOCVA gives us the best and most correct results every time, though it is a more powerful method and reliable.

But again, it depends on data, purpose, and nature of data and several other factors whether the results are correct or not.  


 

Word Cloud for Difference Between ANOVA and ANOCVA

The following is a collection of the most used terms in this article on the ANOVA and ANOCVA. This should help in recalling related terms as used in this article at a later stage for you.

ANOVA and ANOCVA
Word Cloud for ANOVA and ANOCVA

 

References

  1. https://books.google.co.in/books?hl=en&lr=&id=T6uvhsy8d_8C&oi=fnd&pg=PP1&dq=ANOVA+and+ANCOVA&ots=Kk6_p-FneG&sig=gWRRFRZotXiEgjOpIIUPrFG2eX8&redir_esc=y#v=onepage&q=ANOVA%20and%20ANCOVA&f=false
  2. https://journals.sagepub.com/doi/abs/10.1177/0163278703255248
  3. https://link.springer.com/article/10.1007/BF02294394
  4. https://eric.ed.gov/?id=ED222522

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