I need to explain the intuition behind what ANOVA is doing to a non-technical person. Is there a visual that explains the idea? A visual that illustrates the key idea in the context of a one-way ANOVA with perhaps 3 factor levels might be helpful?
Let us suppose that the person has taken some statistical courses as a student in the distant past but has forgotten the details of even performing a z-test. However, he/she remembers that hypothesis testing is used to check if the observed effects are due to random chance or due to a real change in the parameter of interest.