Patient Puzzlers for Healthcare

E2 in the ER

Dr. Cal L. Sterol, ER administrator for St. Recover in the Long Run Hospital, loved data. His favorite data displays were ones that no one could understand, since their confusion gave him an opportunity to demonstrate his own statistical erudition. He loved the language of statistics even more than he loved the clinical jargon that surrounded him in the ER. After all, everyone understood the medical vocabulary, but statistics was something else.

As an inveterate namedropper, Cal would point to the endless displays of clinical data that hung in the ER administrative office, mumbling terminology that no one understood. “Oh, that chart demonstrates kurtosis and skewness in the process,” he would declare. When necessary, he would obfuscate the meaning of the data even further, by mixing terminology that had little to do with analysis.

So when he had an opportunity to learn about control charts and their application in health care environments, he leaped at the chance to attend a seminar on the topic. The instructor introduced control limits and taught participants how to calculate them. Although this was a fairly straightforward process, Cal was already thinking about ways to confuse his colleagues with the formula when the instructor explained individual moving range charts, and the role that E2 plays in calculating control limits. “Bingo!” thought Cal.

Upon his return to the hospital, Cal held forth to whoever would listen, dropping X-bar and R chart terminology, and sprinkling E2 through his conversation. He was caught short, however, when one of the ER nurses asked him to explain the difference between E2 and A2 in calculating the control limits for the individuals. His resourcefulness provided an immediate response—one that left the nurse shaking his head—but Cal himself did not understand the distinction. Can you help him with this one? Which of the following is correct?

A) A2 is the correct factor to use because it comes alphabetically before E2 , and one should use the first appropriate factor. 

B) E2 is the correct factor because it estimates three sigma above and below the mean (X-bar)

C) For individual moving range charts, A2 and E2 will give the same answer

B is the correct answer.

In manufacturing with its emphasis on mass production, X-bar and R charts are the most common form of control charts. Each sample is at least of the size of 2, and 5 is the most common sample size. In these cases, upper and lower control limits are calculated by these formulas:

A₂ is a weighting factor that is used to estimate the upper and lower control limits such that they will be three standard errors above the process average, and three standard errors below the process average. 

Standard error =

There are applications of X-bar and R charts in health care, but individual moving range charts are far more common (sample size = 1).

One might track the blood pressure or cholesterol levels of a patient on a daily basis, or any other critical measure. In charting this data, a different weighting factor is used, known as E₂.

where

UCL_X = upper control limit for the individuals

LCL_X = lower control limit for the individuals

k = number of samples

E₂ = the weighting factor used to estimate three standard deviations above and three standard deviations below the process average.

Dr. Cal L. Sterol may be a great health care administrator, but when it comes to statistics, his number is up.