To The Editor:
In the article "Current Concepts Review. Sample Size and Statistical
Power in Clinical Orthopaedic Research" (81-A: 1454-1460, Oct. 1999),
Freedman and Bernstein refer to the Knee Society score as a continuous
variable when calculating necessary sample sizes. However, this
is not true, as distinct numbers are given to certain levels of
performance or qualities examined; for example, unlimited walking
is given 50 points, walking more than ten blocks is given 40 points,
and walking five to ten blocks is given 30 points2.
This is similar to the system of school grades (A to F) or to the
Apgar score in obstetrics.
The distinction between continuous variables and discrete variables
is important, as the investigator is dealing with different scales
of measurement - namely, with an ordinal scale as opposed to a period
of time as a truly continuous scale of measurement1. Even though ordinal scales of measurement, like
clinical scores, are frequently statistically handled as numerically
scaled data, this is a potential pitfall when choosing the appropriate
statistical test or determining the effect size and consequently
the sample size3.
A. Pingsmann, M.D.
Department of Orthopaedics
Essen Medical School
Hufelandstrasse 55
D-45239 Essen, Germany
K. B. Freedman and J. Bernstein reply:
We thank Dr. Pingsmann for his close and detailed reading of
our article, and we appreciate his comments.
Dr. Pingsmann is technically correct: the Knee Society score
is not a continuous variable but rather an ordinal variable. As
such, nonparametric statistical tests should be used for its analysis. Nonetheless,
for the purpose of assessing sample size, the Knee Society score
behaves like a continuous variable, and the same parameters must
be specified: namely, alpha, beta, effect size, and variance.
We wish that everyone were as keen and aware as Dr. Pingsmann
regarding statistical details. In that case, simplifications would
be unnecessary. On the other hand, because only 5 percent of the articles
that we examined included sample-size calculations or power analyses,
we believe that simplifications (such as glossing over the distinctions
between continuous and ordinal variables) are probably welcome and
acceptable.
Kevin B. Freedman, M.D., M.S.C.E.
Joseph Bernstein, M.D., M.S.
Corresponding author: Joseph Bernstein, M.D., M.S.
Penn Orthopedic Institute
University of Pennsylvania School of Medicine
Hospital of the University of Pennsylvania
424 Stemmler Hall
Philadelphia, Pennsylvania 19104-6081