Patient Puzzlers for Healthcare

Coefficient of variation

Dr. Noah Tahl has learned about the use of control charts, standard deviations, and histograms in a workshop he attended at a national conference of the Institute for Healthcare Improvement. He has seen for himself how these concepts help hospitals and other health care institutions to organize and analyze their data, and is determined to use statistical process control to improve measures of quality at St. Maybe Hospital. In this effort, he engages his staff in a training effort to assure that all members of his department will be on the same page when it comes to statistics.

And speaking of pages, he keeps at least a page ahead of the group that he is training in these methods. So while everyone else may be on the same page, Dr. Noah Tahl stays up late at night to assure himself that he knows more than those whom he is training.

After he has demonstrated the formula for calculating standard deviation and shown his trainees how control charts will help them understand processes, he introduces CHARTrunner, a software program that creates charts from data in established spreadsheets such as Excel. “This will make your life easier,” he promises, but as it turns out, it may be on the verge of making his life harder. Alec Smart, one of his department managers, comes across the concept of the coefficient of variation as he explores the printout of his charted data. He asks Dr. Noah Tahl to explain.

Although this chapter on coefficient of variation is not one that Dr. Tahl has studied yet, he feels compelled to respond, especially since the entire class is looking expectantly at him and waiting for his answer. “That’s really the sum of the log of the standard deviation,” he mumbles. Although no one understands what he means, trainees nod their heads and take notes.

Was this the right definition for coefficient of variation? If so, was Dr. Noah Tahl’s response an inspired guess or an intuitive speculation? Is it important in health care? Stay tuned to learn more about this exciting turn of events in the life of Dr. Noah Tahl, statistician.

Is he correct? Select one of the following responses:

A)  the capability of a process;

B)  whether a process is in or out of control;

C)  the peakedness of a distribution;

D)  the ratio of a mean to a standard deviation in a data set.

D is the correct answer.

Coefficient of variation is a measure of how much variation exists in relation to the mean, so it represents a highly useful—and easy—concept in data analysis. But Dr. Noah Tahl’s guess was a meaningless collection of jargon that he had picked up from a variety of sources. By obfuscating this simple technique, he was in fact robbing his trainees of the opportunity to gain another tool for data analysis.

Coefficient of variation  =

The standard deviation alone is sometimes not particularly useful, without a context within which one can determine meaning. For example, knowing that the standard deviation is 1.76 has no meaning; but understanding that a standard deviation of 2 had been anticipated gives a context that recognizes that variability is less than expected. Knowing that the standard deviation has historically been .5 or less for a particular dimension, on the other hand, 1.76 would be considered high. Without perspective, the figure for standard deviation has limited meaning.

The coefficient of variation provides a reference, by looking at the ratio of a standard deviation to a mean.

Coefficient of variation  =

If the number is large, the data has a great deal of variability with respect to the mean.

e.g., C.V. =

=

= .5

If the number is smaller, this reflects a small amount of variability relative to the mean.

e.g., C.V. =

=

= .05