It is crucial that beginners in basic ANOVA understand the concepts behind ANOVA. Like all statistics calculations, ANOVA is based on the testing of hypothesis. ANOVA seeks to find if the variance introduced into an experiment is the same or less than the normal variations that would result from human error in measurements. A basic concept of ANOVA is that an appropriate ANOVA model must formulate tests to compare the sources of variance in an experimental setting.
Basic ANOVA calculations are all based on the F-ratio. The F-ratio has a null hypothesis of one and is calculated from dividing the variance from an experimental treatment by the variation from an experimental error. If the F-ratio calculation reveals that this ratio is significantly different from one, then the hypothesis is usually thrown out.
Graphical representation of ANOVA is important for allowing students to fully understand how the analysis works. Peaks represent the test and hypothetical data, and examining these peaks shows how the size of variation between samples can be compared with the size of variation within samples, a crucial principle of ANOVA.
Most ANOVA calculations are too complicated to be carried out on regular calculators. Because of this, ANOVA problems are typically worked out through statistics programs like Minitab; training in and knowledge of Minitab or any like program is very important to successfully performing ANOVA tests. While Microsoft Excel can also be used for ANOVA, it may be more difficult to use than Minitab because it is not specifically designed for ANOVA calculations.
There are many variations of ANOVA. Generally speaking, most basic ANOVA problems follow one-way ANOVA between groups or one way repeated measures. More complicated ANOVA calculations might focus on two-way problems or even ANOVA parametric or non-parametric tests.