What is ANNOVA | Analysis of Variance | One Way ANNOVA Test | 7 Steps for ANNOVA

ANNOVA is an inferential statistical method to find out the difference between two data sets. It is a most useful test methodology among researchers and data analyst. ANNOVA is used for the fields of research and study like economics, statistics, biology, psychology and marketing study and many more. It can be performed by manual calculation or with any tools. ANNOVA calculation option is available with analytics or statistical tools like Microsoft Excel, R, Python, SPSS. In this article, we’ll discuss what is ANNOVA or Analysis of Variance. Moreover, Steps of ANNOVA and its types will be discussed.

What is ANNOVA

ANNOVA stands for analysis of variance. As mentioned earlier that it is to check the difference between two data sets or groups. In other words, ANNOVA is being used to check the outcome of an experiment or to check the effect of marketing campaign as example. For the example, one marketing campaign has been done for a FMCG product. To measure the effect, ANNOVA should be applied. In this case, before the campaign data should be measured with after campaign data. Though, the difference is being measured with the help of variance among two data sets, it is called analysis of variance.


If we want to explain ANNOVA by using regression concept, ANNOVA is being used to check the impact of independent variable on dependent variable (two way ANNOVA). ANNOVA is the developed version of t-test and z-test.

Formula of ANNOVA

F= MST/MSE. In the formula, F is the coefficient of ANNOVA, MST stands for mean sum of squares due to the treatment and MSE stands for mean sum of squares due to error.

7 Steps for ANNOVA

  1. First step is to calculate the mean values from data set
  2. Determine null hypothesis and alternate hypothesis with alpha
  3. Calculate the SST or sum of squares
  4. Next step is to calculate “df” or degree of freedom
  5. Calculate to find out Mean squares
  6. Calculate to find out F Statistics
  7. Final step is to look into statistical summary table and arrive at conclusion

Types of ANNOVA

There are two types of ANNOVA based on the number of independent variable. Those are One way ANNOVA and two way ANNOVA. One way or two way ANNOVA is being decided based on the number of variables used in a group. On the other hand, each type can be subdivided into three types, Type I, Type II and Type III.

If you are using statistical tool to perform ANNOVA, each tool will use different type. In case of R it is using Type I, in case of Python it is using Type II and in case of SAS it is using Type III.

One Way ANNOVA Test

In case of one-way ANNOVA, only one independent variable is used to perform the test. Basically, to check the effect of any marketing campaign or variable within one group, one-way ANNOVA is used. To perform the same, three or more samples should be considered. There are some assumptions related to one-way ANNOVA. First assumption is that the sample is selected from a population which is normally distributed. Moreover, the variance of the equality should be same within different groups.


It is a type of hypothesis test. In other words, null hypothesis or alternate hypothesis can be checked with one way ANNOVA.

Null hypothesis (H0): If the mean between two groups are same, null hypothesis is accepted. Alternate hypothesis (H1): If the mean is different between groups, alternate hypothesis is accepted.

To check the hypothesis, p-value plays the key role to reject null hypothesis and accept alternate hypothesis. If the value of p is <0.05, null hypothesis is rejected and alternate hypothesis is accepted. From the ANNOVA output or ANNOVA statistical summary table, p-value can be find out. P-value is the result of F statistics in ANNOVA.

Two Way ANNOVA Test

In case of two way ANNOVA, two variables are used. To check the interaction between variables or factors, two way ANNOVA is used. To perform two way ANNOVA, multiple samples should be considered for each of the variables. Assumptions considered for two way ANNOVA is like, the sample is drawn from a population which is normally distributed. Moreover, the homogeneity is followed of the variance.

One way or two way ANNOVA name has been given based on the variables used for a test as discussed earlier. If the variables are three, it is called three way ANNOVA.

Factorial ANNOVA

Factorial ANNOVA is another name of two-way ANNOVA where more than one independent variables are used which are categorical in nature.


Both ANNOVA and MANNOVA are doing calculation based on mean. The full form of ANNOVA discussed earlier and full form of MANNOVA is multivariate analysis of variance.

In ANNOVA, only one dependent variable is being used for mean calculation. On the other hand, in MANNOVA, multiple dependent variables are used to calculate mean.

There are three methodologies or models for ANNOVA (Type I/II/III) where in MANNOVA there is no such different methodology.

To determine the significance of the ANNOVA test, F-test result is the determining factor. Where in MANNOVA, multivariate F-test (Wilk’s Lambda) is the determining factor.

ANNOVA vs. T-test

It is one of the frequently asked question that when to ANNOVA and when to use T-test. It may create confusion to decide which technique is to be used for mean comparison. Let’s discuss to make it clear.

When test needs to be done between two groups or population, T-test is being used. On the other hand, when number of groups or population are more than two, ANNOVA technique is used.

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