User:Mr. Comodor

Krackow's $$\frac{3}{n}$$ Rule
Krackow's $$\tfrac{3}{n}$$ Rule (also known as "The Statistical Power of Good Results") was developed and proven by Dr. Kenneth A. Krackow. The rule offers a valid statement about the likelihood or probability (p) of an event or outcome that has not occurred after n trials. Consider, 50 trials or occurrences of a particular surgical procedure without observing any cases of wound infection. Further, select a Type I error level of p ≤ 0.05. Then one can say that these data are consistent with the hypothesis that the likelihood of infection for this particular surgery in such patients is ≤  $$\tfrac{3}{n}$$. In this case we are talking about a probability of $$\tfrac{3}{50}$$ or 0.06. The result is proven by examining (1-p)n, n an integer, selecting increasing values for n, and solving for p. One sees that p is approximately equal to $$\tfrac{3}{n}$$. Using L'Hopital's Rule it is possible to show that (1-3/n)n converges to $$\tfrac{1}{e 3 }$$ which serendipitously equals 0.0498, obviously close to 0.05. Another practical application can arise in standard studies comparing groups getting different treatments. If one is concerned that a particular treatment has a higher than desirable chance of a terrible complication such as death, when there has not been a death, one can examine the size of the group and apply this rule. The absence of death after trials of 1,000 patients may not be too reassuring. $$\tfrac{3}{1,000}$$ or 0.3% might be an unacceptably high death rate, and at this size of group we have not eliminated probabilities less than 0.03%. e3
 * x = e is the base of the natural logarithm scale.

= Kenneth A. Krackow, MD =

Kenneth Alan Krackow (b. September 6, 1944) is a world-known orthapedic surgeon and inventor. He is currently Professor of Orthopaedics on the Full-time Faculty at the State University of New York at Buffalo and is Department Head, Orthopaedic Surgery for the Kaleida Health System in Buffalo, New York. He was previously Professor of Orthopaedics at Johns Hopkins University and Medical Institutions, on that full-time faculty from 1978 to 1992 when he moved to Buffalo. His was a public school education until college at Johns Hopkin University (1962-1966). There, he completed a liberal arts major with a concentration in mathematics, before attending the Duke University School of Medicine in Durham, North Carolina (1966-71). There, he obtained his MD degree, and completed one year of graduate mathematics study.

Krackow's full-time activities have principally involved performing and teaching orthopaedic surgery within the subspecialty, lower extremity reconstruction, mainly hip and knee replacement, also referred to as hip nad knee arthoplasty. He has published many peer reviewed articles, written the most widely circulated book on the techniques of performing total knee replacement, and lectured widely also doing demonstration surgery in a large number of foreign countries. As a department head in a large teaching hospital system, he also deals with a large variety of administrative issues.