If our independent variable had no effect, the grand mean would describe the data about as well as three separate means, one for each of the three separate groups. But imagine what would happen if the independent variable really did have an effect on the value of the mugs. We could still compute an overall grand mean that would represent an average for all the groups: however, the means of the individual groups would be quite different from the grand mean. They would also be quite different from one another.