Speaking of Statistics .
Tom Lang Communications
Finely crafted medical writing-
Because publication is the final stage of research.
13 June 2001
|In his 25 years as a medical and
technical writer and editor, Mr Lang has been the Senior
Scientific Writer at the New England Medical Center, the
Manager of Medical Editing Services at the Cleveland
Clinic, Senior Grants Officer at California State
University, Chico, and a technical writer and editor at
Lawrence Livermore Laboratory.
Mr Lang has taught
medical writing at the University of Chicago, at Beijing
Medical University, and at meetings of the American
Medical Writers Association. He is now the President of
the Council of Science Editors.
Mr Lang's 1997 book "How to Report Statistics in
Medicine: Annotated Guidelines for Authors, Editors, and
Reviewers" is the most complete and authoritative
reference in its field.
Mr. Lang has kindly provided the following summary of his
1. Levels of Measurement
- Nominal level: data in named categories
that cannot be ranked, such as blood type (A, B, AB, and
O), or sex (male or female).
- Ordinal level: data in named categories
that are ranked, such as mild, moderate, and severe
disease or test scores that are either high or low.
- Continuous level: data that are measured
on a scale of equal intervals and that, when graphed,
form a distribution, such as weight in kilograms or
concentrations in grams per deciliter.
- Categorical or qualitative data: nominal
and ordinal data
- Semi-quantitative data: ordinal data
- Quantitative data: continuous data
2. Definitions of "Normal"
- Typical, expected: "Everything was
- Healthy; without illness or disability:
"He was a normal boy."
- A "bell-shaped" distribution of data:
"The data were normally distributed."
- A diagnostic test result in a range of values indicating
the absence of disease (a therapeutic definition of
- A diagnostic test result in the central 95% of a range of
values; results in the upper or lower 2.5% of the range
are "abnormal" (a statistical definition of
- A diagnostic test result in the lowest (or highest) 95%
of a range of values; results in the remaining 5% of the
range are "abnormal" (another statistical
definition of "normal")
3. Standard Deviation and Standard Error of the Mean
- Standard deviation (SD): the variability
of data from a sample. To be used (with the mean) only
when describing normally distributed data. The SD is a
- Standard error of the mean (SEM): the
precision of an estimated population value. Reported only
in predictive models. The SEM is an
- The SEM is always smaller than the SD, so it is often
reported to make measurements look more precise. However,
the mean and SD are preferred for describing a
distribution of data.
- The SEM is about a 68% confidence interval (CI). However,
the 95% CI is preferred for reporting the precision of an
4. Median and Interquartile Range
- Median: the value that separates the
upper half of the data from the lower half; the value at
the 50th percentile
- Interquartile range (IQR): the values at
the 25th and 75th percentiles and the difference between
- Median and IQR are useful for describing any
distribution, especially non-normal distributions.
- Most biological data are not normally distributed.
5. Parametric and Nonparametric Tests
- Parametric tests: statistical tests that
assume the data are normally distributed. Example: t test
- Nonparametric tests: statistical tests
that do not assume the data are normally distributed.
Example: Wilcoxon's rank-sum test
- Authors should always say whether the assumptions of the
statistical tests were met by the data.
6. "Alpha" Error and Statistical
- If patients respond to a drug, we must decide whether the
response is the result of the drug or of chance. Alpha is
the probability that we will be wrong if we say that the
drug is effective.
- Alpha: defines statistical significance.
Alpha is usually set at 0.05 or 0.01. By definition,
P values above the alpha are not statistically
significant; those below are.
- The P value is a measure of the evidence
against chance as an explanation for the result. The
lower the P value, the less the evidence for chance, and
therefore the greater the evidence for non-chance as an
- P values say nothing about the medical importance of the
results: authors should not confuse statistical
significance with clinical importance!
7. Multiple (Pairwise) Comparisons; Multiple Testing;
Multiple "Looks" at the Data
- When alpha is 0.05, 5 of every 100 P values will be
statistically significant by chance.
- When several P values are calculated from the same data
(a process called "multiple testing"
or "multiple looks at the data"),
the probability that some of these P values will be
statistically significant by chance is increased to above
- Comparing 6 groups to one another two at a time requires
15 "pairwise" comparisons. Here, alpha rises
from 0.05 to 0.55. That is, one of every two P values is
likely to be statistically significant just by chance,
not because the groups are different.
- This rise in probability can be adjusted for with
"multiple comparison procedures" or
corrections, such as the Bonferroni correction.
8. "Beta" Error and Statistical Power
- If patients do not respond to a drug, we must decide
whether the drug is not effective or whether enough data
were collected to find a difference. Beta is the
probability that we will be wrong if we say that the drug
is not effective.
- Beta (ß) is usually set at 0.02 or
0.01 but is most often expressed as statistical power, or
1 - ß. A statistical power of 80% or 90% is common.
Power is related to sample size: were enough patients
studied to find a difference if there was one to find?
- Many "negative" studies (those without
statistically significant results) are actually
inconclusive because they are "underpowered:"
they did not collect enough data to proove that the drug
was not effective. "Absence of proof is not proof of
9. Random, Randomized, Randomization
- "Random:" without a pattern;
entirely the result of chance
- In a "randomized trial,"
patients are randomly assigned to a treatment or to a
control group to prevent bias.
- Researchers first create a "randomization
schedule," or a list of random numbers,
each of which is associated with either the control or
the treatment group. How this schedule was created should
- This schedule is used to assign each patient to a group
when they are enrolled in the trial.
- The schedule should be hidden from those assigning
patients to groups, to prevent bias. This process is
- Patients are not "randomized," they are
randomly assigned or assigned at random.
10. "Blinding" and "Masking"
- Blinding: the process of hiding
assignment to the treatment and control groups from
patients, researchers, and sometimes even from
statisticians to prevent expectation bias.
- Masking: the same as
"blinding." Some authors prefer
"masking" to "blinding" because of
the medical condition of being without sight. Either term
- Single-blinded, double-blinded, and triple-blinded trials
should say which groups were blinded.
Terms Relating to Patients
- Patients do not "develop a disease," the
disease develops in patients.
- Patients are not "diagnosed" with a disease,
diseases are diagnosed in patients.
- Patients do not "complain of symptoms," they
report having symptoms.
- Adult patients are "men and women," and
children are "boys and girls," not "male
and female." Male and female can be used for infants
and when patients include adults and children.
- Patients do not "fail the treatment," the
treatment fails in the patient.
- The patient is a patient, not a "case." A case
is an instance of a disorder or disease.
- Test results are not "suspicious," they are
- Everitt BS. The Cambridge Dictionary of Statistics in
the Medical Sciences. London: Cambridge University
- Lang T, Secic M. How To Report Statistics in
Medicine: Annotated Guidelines for Authors, Editors, and
Reviewers. American College of Physicians, 1997.
- Last JM, editor. A Dictionary of Epidemiology.
London: Oxford University Press, 1988.
- Schwager, E. Medical English Usage and Abusage.
Phoenix, Arizona: Oryx Press, 1991.
- Vogt WP. Dictionary of Statistics and Methodology: A
Nontechnical Guide for the Social Sciences. Newbury
Park, California: Sage Publications Inc., 1993.
index of past meetings]