## ANOVA, ANCOVA, MANOVA & MANCOVA: Statistical Soup

I bet there is hardly anyone who wouldn’t feel trapped when it comes to the Statistical Soup! Okay, let me be little more clear to you. We are talking about the ANOVA, ANCOVA, MANOVA and MANCOVA, yeah this is the Statistical Soup!
Students are usually confused and bamboozled when it comes to make comparisons between ANOVA, ANCOVA, MANOVA and MANCOVA. It is very imperative to know the similarities between various factors before we can draw some distinctions between them. So let's discuss the analogy among them first.

ANOVA
ANOVA stands for Analysis of Variance, as it is one of the core elements of all the four analysis. An ANOVA has only one dependent variable. In stats, when two or more than two means are compared simultaneously, the statistical method used to make the comparison is ANOVA. It imparts results and values which can be checked to find out whether any relation is there between different variables. If we have to determine whether the means of two or more groups are equal, then ANOVA comes to our rescue through a test known as T-test. ANOVA can compare the means simultaneously as it is very helpful in avoiding TYPE 1 error while carrying out multiple, two sample tests. It has got one more special feature as it compares scale or interval variables, also known as continous variables.
ANOVA has three different models
Fixed effect model--- is subjected to one or more than one treatment to find out if the value of the response variable changes.
Random effect model---- is applied where the treatment applied to the subject is not fixed.
Mixed effect model-----it has got both fixed effect and Random effect which is applied to experimental factors.

ANCOVA
Now what is the difference between ANCOVA and ANOVA. A layman's answer would be the letter "c". But there is obviously much difference between ANOVA and ANCOVA as the latter has single continuous response variable. ANCOVA makes a clear comparison between response variable with both continuous independent variable and factor. Covariate is the term to denote the continuous independent variable in ANCOVA. It is not that ANCOVA is limited to above mentioned comparative analyses as it can also analyse with a single response variable, continuous IVs with no factors. Such an analysis is also called REGRESSION. We can get similar outputs in SPSS by conducting this analysis using "Analyze>Regression>Linear" dialog menus or "Analyze > General Linear Model (GLM) > Univariate" dialog menus.

MANOVA
In stats, it contains multiple dependent variables. MANOVA helps in determining the distinctions between two or more than two dependent variables simultaneously. MANOVA determines interactions taking place between dependent as well as independent variables. Actually MANOVA is another type of ANOVA having two or more continuous variables. If we want to compare two or more continuous response variables by a single factor then one way MANOVA is useful, whereas two way MANOVA includes two or more continuous response variables by comparing them with at least two factors.
Another difference between MANOVA and ANOVA is that ANOVA uses an independent T-test while dealing with single response variable and binary factor. But a t-test cannot calibrate distinctions for more than one response variable together.

MANCOVA
Here again, this letter "c" creates an obvious difference between MANOVA and MANCOVA as it is in the case of ANOVA and ANCOVA, where 'c' again denotes Covariance. MANOVA and MANCOVA show two or more response variables, but the major difference between them is characteristics of IVs. MANCOVA compares two or more continuous response variables by levels of factor variables along with a covariate.

I hope the much confusion is resolved now about the Statistical Soup. In case you still have any doubt, kindly post your queries below in the comment box.

Category : PhD Statistics