# Some resources for Analysis of Means

## 2006-06-30

One of the techniques recommended by Davis Balestracci when he visited CMH in June 2006 was Analysis of Means, which often is abbreviated ANOM. You can use ANOM much like a control chart, but it is applied when you have a collection of averages representing the performance of specific subgroups. The classic application is examining the performance of several different workers who are all performing a similar task. I tend to dislike examples like that because it implies that the root cause of most problems lies in the workers themselves. That’s not really true, though, but even if it were, such a focus early on in a quality program would lead to a lot of resistance, defensiveness, and possibly even fudging the numbers.

Still, ANOM is a useful tool that has a lot of profitable applications.

The first thing you might notice is the similarity between the acronym ANOM and another acronym, ANOVA (Analysis of Variance). The two approaches can be used on the same problem, but they have a different focus. In ANOVA, the comparison is typically to see if certain levels of a factor differ from other levels of a factor. In ANOM, the comparison is typically to see if certain levels of a factor differ from the overall mean. You can adapt ANOVA to perform the latter task, but it is typically not done all that often. The other difference is that ANOM will typically use a graphical display that looks much like a control chart.

Here is a nice resource for ANOM

A brief tutorial for ANOM is available at

that shows how to use MINITAB for ANOM. Most software programs do not have ANOM.<U+FFFD> (I know for sure that R, SPSS, and STATA do not have it) but instead provide the results of the ANOVA model instead. Apparently, ANOM is available in the SAS/QC package.

Donald Wheeler is one of my favorite authors, and you can find a nice discussion of ANOM in Chapter 18 of

• Advanced Topics in Statistical Process Control: The Power of Shewhart’s Charts. Donald J. Wheeler (1995) Knoxville, Tennessee: SPC Press. [BookFinder4U link]

(Update: 2007-02-01). The best book on this topic is

• The Analysis of Means. Nelson PR, Wludyka PS, Copeland KAF (2005) Philadelphia, PA: SIAM. ISBN: 0.89871.592.X. [BookFinder4U link]

An interesting review of this book is on the web in PDF format at

You can find the table of contents, introduction, and first chapter of the book on the web in PDF format at

The first<U+FFFD> chapter includes several simple examples. The first example shows paint drying times for four different types of paint. The data (mean +/- sd) are

• 6.88 +/- 1.72
• 9.28 +/- 1.85
• 9.00 +/- 2.81
• 9.90 +/- 1.95

Each paint type was tested four times, for a total of 16 observations. The overall mean is 8.8 and the lower and upper decision limits are 7.0 and 10.5, respectively. When I get some time, I’d like to replicate this example using R software.