One-way analysis of variance (ANOVA) is a method for testing whether three or more populations have the same mean value. One-way ANOVA is used when quantitative data has been collected from 3 or more independent samples. The analysis involves two variables: the independent variable, which is a factor identifying individuals as belonging to one of three or more groups being compared and the dependent variable, a quantitative variable which is being compared between the three samples.

The null hypothesis states that all the populations have the same mean whereas the alternative hypothesis states that not all means are the same. The alternative hypothesis therefore states that ‘at least two means’ are different. The alternative hypothesis could be true if just one mean is out of line with the rest or if all of them are different to each other. At the conclusion of the test, if the null hypothesis is rejected, then further tests, called ‘post hoc tests’, may be used to determine which means differ significantly from each other.

Two-way or three-way analysis of variance extends this technique to analyses where two or more factors can influence the dependent variable. There are also procedures for applying ANOVA to data from related samples or ‘repeated measures’ data.

Analysis of variance is a PARAMETRIC method. It is based on the assumptions that the data is Normally distributed within each group and that the variance is the same within each group.

Example PDF »