Analysis of variance (ANOVA) is a collection of statistical models used to analyze the differences between group means and their associated procedures such as variation among groups. ANOVA provides a statistical test of whether or not the means of several groups are equal. Doing multiple two-sample t-tests would result in an increased chance of committing the type I error (false positives leading to false scientific claims). For this purpose, ANOVAs are useful in comparing (testing) three or more means (groups or variables) for statistical significance.
ANOVA generalizes to the study of the effects of multiple factors. Factorial analysis of variance is when the experiment includes observations at all combinations of levels of each factor. The Factorial ANOVA task enables us to perform an analysis of variance when you have multiple classification variables. It is an inferential statistical test that allows you to test if each of the several independent variables have an effect on the dependent variables. It also allows you to determine if two or more independent variables interact with each other.
An important feature of Factorial ANOVA is that the statistical significance of the experiment is determined by a ratio of two variances. This ratio is independent of several possible alterations to the experimental observations: Adding a constant to all observations does not alter significance neither does multiplying all observations by a constant alter significance. So ANOVA statistical significance results are independent of constant bias and scaling errors as well as the units used in expressing observations
Factorial analysis of variance is determined using softwares such as MS-Excel and SPSS.