# Understanding Analysis of Means

## What is Analysis of Means?

Analysis of means is a graphical alternative to ANOVA that tests the equality of population means. The graph displays each factor level mean, the overall mean, and the decision limits. If a point falls outside the decision limits, then evidence exists that the factor level mean represented by that point is significantly different from the overall mean.

For example, you are investigating how temperature and additive settings affect the rating of your product. After your experiment, you use analysis of means to generate the following graph.

## Comparison of Analysis of Means (ANOM) and ANOVA

ANOVA tests whether the treatment means differ from each other. ANOM tests whether the treatment means differ from the overall mean (also called the grand mean).

Often, both analyses yield similar results. However, there are some scenarios in which the results can differ:
• If one group of means is above the overall mean and a different group of means is below the overall mean, ANOVA might indicate evidence for differences where ANOM might not.
• If the mean of one group is separated from the other means, the ANOVA F-test might not indicate evidence for differences whereas ANOM might flag this group as being different from the overall mean.

One more important difference is that ANOVA assumes that your data follow a normal distribution, while ANOM can be used with data that follows a normal, binomial, or Poisson distribution.