Analysis of variance (ANOVA) is a collection of statistical methods used to analyse the differences between group means which may include one or more treatments or structural design features (such as a block) . The variation is partitioned as "variation" among and between groups.

 

In ANOVA  the observed variance in a particular variable is partitioned into components attributable to different sources of variation.

In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalises t-test to more than two groups.

Doing multiple two-sample t-tests would result in an increased chance of committing a Type I error. For this reason, ANOVAs are useful in comparing (testing) three or more means (groups or variables) for statistical significance. Many field trials use ANOVA, and the principles of design are used to set up, amd layout the experiment in the field or glasshouse. Factorial ANOVA allows us to look at two or more factors and the interaction of  two or more factors of interest.

We can use blocking of land, or pots within an experiment to reduce unwanted variation, and remove the effect of gradients on our mean estimates.