0
Correspondence |

# Interpreting the P ValueFREE TO VIEW

Fabien Maldonado, MD; Colin P. West, MD, PhD
Author and Funding Information

From the Division of Pulmonary and Critical Care Medicine (Dr Maldonado) and the Division of General Internal Medicine and Division of Biomedical Statistics and Informatics (Dr West), Mayo Clinic.

Correspondence to: Fabien Maldonado, MD, Division of Pulmonary and Critical Care Medicine, Gonda 18 S, Mayo Clinic, 200 1st St SW, Rochester, MN 55905; e-mail: Maldonado.Fabien@mayo.edu

Financial/nonfinancial disclosures: The authors have reported to CHEST that no potential conflicts of interest exist with any companies/organizations whose products or services may be discussed in this article.

© 2011 American College of Chest Physicians

Chest. 2011;139(3):723-724. doi:10.1378/chest.10-2449
Text Size: A A A
Published online

## To the Editor:

We read with interest the recently published article in CHEST (September 2010) by Harvey and Lang1 on hypothesis testing, study power, and sample size. The authors remind us that although the α level is typically arbitrarily set at 0.05, other values may be important to consider, depending on whether a type 1 error would carry better or worse consequences than a type 2 error in a given study. In addition, as rightly pointed out, statistically significant results do not invariably translate into clinically meaningful results. There is another point, often overlooked, that we would like to emphasize with regard to the P value. We illustrate this through analogy with diagnostic test performance characteristics.

The sensitivity of a clinical test is the probability that the test is positive in a patient who has the disease. Specificity is the probability that the test is negative in a patient without the disease. These diagnostic test characteristics require that disease status already be known. However, patients (and physicians) would usually rather know the probability that a patient has the disease, given a specific test result. This probability can be derived by application of Bayes theorem and an estimate of the pretest probability of disease.

As Harvey and Lang1 note, the P value is the “... probability of observing a result as extreme or more extreme as the one observed...,” if in truth there is no difference between the groups. As for a diagnostic test, this must be contrasted with what we would usually rather know: the probability that the hypothesis tested is in fact true, given the study results. To evaluate this probability, a similar Bayesian approach, incorporating an estimate of the “prestudy” probability that the hypothesis is true, is required.2

The interpretation of the P value should therefore take into account not only rates of type 1 and type 2 error and the consequences that would occur by making them but also the pretest probability that a tested hypothesis is true in the first place. For example, a statistically significant P value (often P < .05) in a study evaluating an improbable hypothesis should be approached with a healthy dose of skepticism. Similarly, a statistically nonsignificant P value, even with adequate power, may not represent strong evidence in support of the null hypothesis if the pretest probability that the alternative hypothesis is true is high.3

## References

Harvey BJ, Lang TA. Hypothesis testing, study power, and sample size. Chest. 2010;1383:734-737. [CrossRef] [PubMed]

Atkins CD. A clinician’s view of statistics. J Gen Intern Med. 1997;128:500-504. [CrossRef] [PubMed]

Ioannidis JP. Why most published research findings are false. PLoS Med. 2005;28:e124. [CrossRef] [PubMed]

## References

Harvey BJ, Lang TA. Hypothesis testing, study power, and sample size. Chest. 2010;1383:734-737. [CrossRef] [PubMed]

Atkins CD. A clinician’s view of statistics. J Gen Intern Med. 1997;128:500-504. [CrossRef] [PubMed]

Ioannidis JP. Why most published research findings are false. PLoS Med. 2005;28:e124. [CrossRef] [PubMed]

NOTE:
Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging & repositioning the boxes below.

• CHEST Journal
Print ISSN: 0012-3692
Online ISSN: 1931-3543