Analysis of Means: A Graphical Method for Comparing Means, Rates and Proportions.
AUTHORS: P. Nelson, P. Wludyka and Karen Copeland
PUBLISHER: SIAM, 2005, Philadelphia
ISBN: 0-89871-592-x.179 pp plus Tables, References, and Index
This spring, I was complaining to a 'real' statistician that there were no tools to compare a series of means. The t-tests are good only for comparing two means, the analysis of variance (ANOVA) can compare several means, but should a difference among them exist, the ANOVA does not identify it. A similar situation occurs with the chi-squared test. My friend suggested I look at the Analysis of Means. And was he right! This is such a nifty tool for us in the laboratory, it's sad to find out about it at this point in my life (and yours). But ... it's not too late for us to use it. (It was first proposed by LaPlace 180 years ago--100 years before the ANOVA was introduced by Fisher.) Let me show you an example:
Suppose you had a set of method comparison data from six methods for d-dimer. You had run the 50 samples by each of the six methods. You plugged the data into your computer (Excel works) and found that the ANOVA said that the six methods were not the same. That is, statistically speaking, one or more of the means differed from the group of six means. You ask which one. Without boring you with the details, at this point you are stuck. Because, without playing unfairly with statistics, all you can say is that there is a difference here, but I don't know which one(s) of the means differs from the set. Enter Analysis of the Means.
You have the means of the six methods and the SDs of each set. You can draw the graph of the means. And using the tables in this book, you can set the limits on the means. Such a graph looks like this.
The x's are the means from each of the methods, the grand mean is the mean of the six means and the limits are based on the SD and the number of samples.
The ANOVA said there was difference; the graph shows two means differing statistically from the set. And I can see it! No fancy math!
Can you not see this for comparing methods in your lab? In an interlab program? Means over time?
Suppose I tell you that this will work with SDs as well as means.
Suppose I have a set of data like this:
Example n n with symptom x Males < 45 yrs 124 11 Males > 45 57 12 Females < 45 153 9 Females > 45 67 10
For this set of data, you might use a chi-squared test to find out if these four groups are the same. Suppose the chi-square says they are not the same, but I cannot tell you which one(s) differ from the group. Again, turn to AOM and the graph will show you.
Know that, while this is graphical, it is not just a pretty picture. It has been demonstrated that the approach is not only pretty but statistically robust (sound). At the AACC meeting in July of 2008, I was privileged to present a poster on this using data from labs like yours and some simulated data (I will be happy to send the poster if you want. Davidplaut@yahoo.com is my e mail address). I also demonstrated the advantages of AOM over ANOVA and chi-squared. If want to have a better handle on a number of your statistics, take a minute and think of the dozens of applications
for which you could use this, and obtain a copy of this clearly written book. It has many examples, not so much math you will give up, and leads you through the process in a pleasant way.
I again thank my friend for pointing me in this direction and the authors for making this available to us all.
Book Reviews are written by David Plaut, 3609 Cross Bend, Plano, TX 75023. firstname.lastname@example.org