When an F value is significant we conclude there is a difference between at least two of the means. But if we are testing a set of three means then there is three possible combinations of pairs any of which or all of which might be different. For this reason, we will also be using POST HOC comparisons to tell us if there is significance. As you can see there are many options. We will use the LSD test to do this.
Analysis of variance is used to test the hypothesis that several means are equal.
Remember the hypothesis saying the means will be equal is called the null hypothesis. If we reject the null, then we can conclude that at least two of the means are different - this is the research or alternative hypothesis. In addition to determining that differences exist among the means, you may want to know which means differ. Contrasts are tests set up before running the experiment, and post hoc tests are run after the experiment has been conducted. You can also test for trends across categories.