Adv Physiol Educ AJP: Heart and Circulatory Physiology
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Advan. Physiol. Edu. 32: 335, 2008; doi:10.1152/advan.90195.2008
1043-4046/08 $8.00
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ADV PHYSIOL EDUC 32:335, 2008
© 2008 American Physiological Society

LETTER TO THE EDITOR

Reply to B. Kay

Douglas Curran-Everett1,2,3 and Dale J. Benos4

1 Division of Biostatistics and Bioinformatics, National Jewish Health, University of Colorado Denver, Denver, Colorado 2 Department of Biostatistics and Informatics, University of Colorado Denver, Denver, Colorado 3 Department of Physiology and Biophysics, University of Colorado Denver, Denver, Colorado 4 Department of Physiology and Biophysics, University of Alabama at Birmingham, Birmingham, Alabama

Address for reprint requests and other correspondence: D. Curran-Everett, Div. of Biostatistics and Bioinformatics, M222, National Jewish Health, 1400 Jackson St., Denver, CO 80206 (e-mail: EverettD{at}njc.org)


   Introduction
TOP
 Introduction
REFERENCES
 
We appreciate the letter from Dr. Kay. We agree it is important to report the statistic appropriate to the inference one wants to make. In fact, two guidelines reinforce this notion:

Guideline 5. Report variability using a standard deviation.

Guideline 6. Report uncertainty about scientific importance using a confidence interval.

But we disagree with Dr. Kay's contention that a single standard error is a useful statistic with which to make an inference about possible values of some population characteristic. It is a confidence interval–not a standard error–that is the thing to use (1, 3–8).

The standard error of the sample mean, SE{y}, does represent the expected variation of possible values of the sample mean y (2, 6), but the interval

Formula

is just a 68% confidence interval (4, 8). It is not especially helpful to declare, with a whopping 68% confidence, that the population mean is included in that interval. It is helpful to report a 90, 95, or 99% confidence interval.

Kay reminds us that, because

Formula 1(1)

we can derive a sample standard deviation s from a standard error of the mean if we know the sample size n. Kay is being generous when he says that the mathematics required to solve Eq. 1 for the standard deviation s is simple. What happens if we want to make inferences about the difference between two sample means? That is, what happens if we want to assess whether the means are similar or different? In this situation, we calculate the standard error of the difference between sample means, SE{Formula 12 – Formula 11}:

Formula 2(2)

where sj2 is the variance and nj is the size of sample j. For even a motivated reader, it is now impossible to derive the standard deviation for each sample: there are a whole lot of paired values of sl and s2 that satisfy Eq. 2.

The message. If variability is important to your scientific observations and inferences, then report the standard deviation. If a range of possible values for some characteristic of a population is important, then report a confidence interval.


   REFERENCES
TOP
 Introduction
 REFERENCES
 

  1. Council of Science Editors, Style Manual Subcommittee. Scientific Style and Format: the CSE Manual for Authors, Editors, and Publishers (7th ed.). Reston, VA: Rockefeller Univ. Press, 2006, p. 167–170.
  2. Curran-Everett D. Explorations in statistics: standard deviations and standard errors. Adv Physiol Educ 32: 203–208, 2008.[Abstract/Free Full Text]
  3. Curran-Everett D, Benos DJ. Guidelines for reporting statistics in journals published by the American Physiological Society. Am J Physiol Lung Cell Mol Physiol 287: L259–L261, 2004.[Free Full Text]
  4. Curran-Everett D, Benos DJ. Guidelines for reporting statistics in journals published by the American Physiological Society: the sequel. Adv Physiol Educ 31: 295–298, 2007.[Free Full Text]
  5. Curran-Everett D, Benos DJ. Last Word on Perspectives "Guidelines for reporting statistics in journals published by the American Physiological Society: the sequel". Adv Physiol Educ 31: 306–307, 2007.[Free Full Text]
  6. Curran-Everett D, Taylor S, Kafadar K. Fundamental concepts in statistics: elucidation and illustration. J Appl Physiol 85: 775–786, 1998.[Abstract/Free Full Text]
  7. International Committee of Medical Journal Editors. Uniform requirements for manuscripts submitted to biomedical journals. Ann Intern Med 126: 36–47, 1997.[Free Full Text]
  8. Lang T. The need for accurate statistical reporting. A commentary on "Guidelines for reporting statistics in journal published by the American Physiological Society: the sequel." Adv Physiol Educ 31: 299, 2007.[Free Full Text]




This Article
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