# Analysis of Variance (ANOVA) - Explained

What is Analysis of Variance?

# What is Analysis of Variance - ANOVA?

Analysis of variance or ANOVA is a statistical analysis tool that separates the aggregate variability that is observable into two parts: Systematic factors that statistically influence a given data set and the random factors which don't.

## How does Analysis of Variance Work?

The ANOVA method is usually applied in instances where the variable is measured in different independent groups. If such a case happens, the variable is checked to see if it is constant or varies between the various groups, and whether it arose from chance or if the variations are a product from which the sample is taken. Therefore this hypothesis is used to test if the mean variations being portrayed in the different groups are similar or different. ANOVA is used in the comparison of two or more means, and this makes it necessary since you cannot use the contrast based the Student t-test to compare more than two means repeatedly because of two reasons:

• The probability of finding a significant variation by chance would increase since there would be several hypothesis contrasts carried out simultaneously and independently. In the null hypothesis, there is a probability that the HO would exceed the critical level, and therefore it would be rejected.
• The null hypothesis is that the two samples are derived from the same population and yet for each comparison, the variance necessary for the contrast is estimated differently since it is done on many different samples.

ANOVA provides a solution to these problems. This method allows for the comparison of several means in different situations that are much linked and to the design of experiments and sometimes the multivariate analysis basis.

## The use of Analysis of Variance ANOVA

This method is useful where more than two groups are available. In the case of only two samples, the t-test can be used in the comparison of the sample media, but if the samples increase to more than two, it could become unreliable. T-test gives identical results as the ANOVA in the comparison of only two samples.

### One-Way ANOVA

For example, a researcher wants to test the effects of 5 different exercises, and he recruits 20 men. He assigns each activity to four men and then records their weights after a few weeks. By comparing the weights of the five groups of men, the researcher can find out if the effects of these exercises were significant on them. This example shows a case of ANOVA of a balanced equation. This type of ANOVA is called one way because only the effects of one category have been studied and balanced since each same number of men is assigned to specific exercise. The basic idea is to determine if the samples are similar or not.

### Can I Use Multiple T Tests?

The t-test is only applicable where there are just two media. However, it is possible to use many T-tests to compare each medium with each other. One should note that multiple t-tests can result in severe complications and in such cases, ANOVA is used. It is used when an alternative procedure is required to test the sample media hypotheses of several populations.