Arachnophobia is the fear of spiders. People with arachnophobia suffer to different degrees, but they tend to react intensely to visible signs of the presence of spiders, such as webs. The director of a clinic decides to investigate different treatment types for arachnophobia. She gathers three groups of clients: One group receives in vivo flooding, which involves prolonged or repeated exposure to the actual anxiety-producing stimuli. The second group receives imaginal flooding, which involves the same techniques as in vivo flooding, except the exposure occurs in the client’s imagination. The third group receives no treatment. The results come in, and a statistician conducts an analysis of variance. The is that there is no difference between the population means (in other words, there is no treatment effect).
The is that at least one of the population means is different from another (in other words, there is an effect Of at least one Of the treatments).