# Analysis of variance

Analysis of variance, or ANOVA (analysis of variance), are multivariate dependency analysis techniques used to determine whether there are significant differences between the means of three or more population groups. Therefore, with this analysis we will find out if there are differences between certain groups when we modify one or more characteristics. To find out, we use the value of the average of the data.

Its use is very frequent in fields such as economics or medicine.

## Previous assumptions of the analysis of variance

There are a number of prerequisites for doing ANOVA that should be known. These are essential for the results to be adequate.

• First, the population must follow a normal distribution. Therefore, we are facing a type of parametric contrast, since the population parameters of the mean and the standard deviation are known.
• Furthermore, the samples used must be independent of each other. This means that a modification in one of them does not have to affect the value of the others.
• On the other hand, the variances of the populations under study must be equal. This is called homoscedasticity.

## Classification of the analysis of variance models

For the analysis of variance models, the three classifications shown below can be used:

• Fixed effects model : Populations are normal and only differ in the value of their respective means.
• Random effects model : In this case, the data have a hierarchy and the population differences depend on it.
• Mixed effects model : We would be facing a model that is a mixture of the previous two.

## ANOVA example: important concepts

There are mathematical equations of some complexity to perform the ANOVA. However, in Economipedia we opted for the simple economy and, therefore, and taking advantage of technology, we are going to show how it could be done in a spreadsheet.

Let’s imagine that we want to know if there are significant differences between Economipedia readers, depending on the affinity of their degree with economics.

Warning: The data we will use is fictitious.

We must go to Data, Data analysis and we will choose the analysis of variance of a factor.

The rank would be the matrix of the three groups. It may be more interesting to include the headings afterwards and give the desired formatting. In our case, with the logo and the color blue.

We see that there are some concepts such as degrees of freedom and probability or significance. The first is calculated automatically and is the number of groups minus one. The second tells us if the differences are significant or not.

Usually you start from an accepted level of trust. In economics it is usually 95% (0.95), which is related to a significance of 0.05 (1-0.095). In this way, if that probability or p value is below the accepted significance, the differences are significant.

In this case, it seems that the degree does not influence the number of readers (significance> 0.05). Therefore, the analysis of variance seems to indicate that Economipedia interests everyone, not just specialized readers. Of course they are fictitious data or not?