**Speaking of Statistics .
. .**

**Tom Lang
**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 presentation.

**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 normal."**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 "normal")
- 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 "normal")
- 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 "descriptive" statistic.**Standard error of the mean (SEM):**the precision of an estimated population value. Reported only in predictive models. The SEM is an "inferential" statistic.- 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 estimate.

**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 them- 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
Significance**

- 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 explanation. - 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 0.5. - 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 absence."

**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 be reported. - 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
"
**allocation concealment**." - 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 is correct.- 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 uncertain.

**References**

- Everitt BS.
*The Cambridge Dictionary of Statistics in the Medical Sciences*. London: Cambridge University Press, 1995. - 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.