Question: How powerful is the ANOVA test in detecting differences between means when you are sure that there are differences? You can explore this question with simulation. Use the generic formula = NORMINV(RAND(),mean,stdev) to generate n random numbers in each of four columns. The numbers in any given column should have the same mean, but the means can vary across columns. The standard deviation should be the same in all columns. (Remember that this is an assumption behind the ANOVA test.)
Do not freeze the random numbers; keep them random. You can choose the means and the common standard deviation. Run the ANOVA test on the randomly generated data. Because the ANOVA outputs are linked to the data, the results will change each time you recalculate with the F9 key. Try a number of settings for the means and report the results. For example, you could make all of the means different but very close to one another, you could make them all far apart from one another, you could make three of them equal and the fourth equal to some other value, and so on. Explain whether the results go in the direction you would expect. Is the ANOVA test very powerful in detecting mean differences?