P Values: Everything You Know Is Wrong

The Gist:  P values are probably the most “understood” statistic amongst clinicians yet are widely misunderstood.  P values should not be used alone to accept or reject something as “truth” but they may be thought of as representing the strength of evidence against the null hypothesis [1].

Part of our 15 Minutes - 'Stats are the Dark Force?' residency lecture series

P: Everything You Know Is Wrong from Lauren Westafer on Vimeo.

At various times in my life I, like many others, have believed the p value to represent one of the following (none of which are true):

• Significance
• Problem:  Significance is a loaded term.  A value of 0.05 has become synonymous with “statistical significance.”  Yet, this value is not magical and was chosen predominantly for convenience [3].  Further, the term “significant” may be confused with clinical importance, something a statistic cannot answer.
• The probability that the null hypothesis is true.
• Problem: The calculation of the p value includes the assumption that the null hypothesis is true.  Thus, a calculation that assumes the null hypothesis is true cannot, in fact, tell you that the null hypothesis is false.
• The probability of getting a Type I Error 
• Background: Type I Error is the incorrect rejection of a true null hypothesis (i.e. a false positive) and the probability of getting a Type I Error is represented by alpha. Alpha is often set at 0.05 so that there is a 5% chance you are wrong if you reject the null hypothesis. This is a PRE test calculation (set before the experiment)
• Problem: Again, the calculation of the p value assumes the null hypothesis is true. The p value only tells us the probability of getting the data we did, it does NOT speak to the underlying truth of whatever is being tested (i.e. efficacy). The p value is also a POST test calculation.
• The error rate associated with various p values varies, depending on the assumptions in the calculations, particularly prevalence. However, it's interesting to look at some of the estimates of false positive error rates often associated with various p values:  p=0.05 - false positive error rate of 23-50%; p=0.01 - false positive error rate of 7-15% [5].

P value is the probability of getting results as extreme or more extreme, assuming the null hypothesis is true. Originally, this statistic was intended to serve as a gauge for researchers to decided whether or not a study was worth investigating further [3].  

• High P value - data are likely with a true null hypothesis [Weak evidence against the null hypothesis]
• Low P value - data are UNlikely with a true null hypothesis [Stronger evidence against the null hypothesis]

Example:  A group is interested in evaluating needle decompression of tension pneumothorax and proposes the following:

• Hypothesis - Longer angiocatheters are more effective than shorter catheters in decompression of tension pneumothorax.
• Null hypothesis - There is no difference in effective decompression of tension pneumothorax using longer or shorter angiocatheters.

A group, Aho and colleagues, did this study and found a p value of 0.01 with 8 cm catheters compared with 5 cm catheters.  How do we interpret this p value?  

• We would expect the same number of effective decompressions or more in 1% of cases due to random sampling error.  
• The data are UNLIKELY with a true null hypothesis and this is decent strength evidence against the null hypothesis.

Limitations of the Letter “P”

• Reliability.  P values depend on the statistical power of a study. A small study with little statistical power may have a p value greater than 0.05 and a large study may reveal that a trivial effect has statistical significance [2,4].  Thus, even if we are testing the same question, the p value may be "significant" or "nonsignificant" depending on the sample size.
• P-hacking.  Definition:  "Exploiting –perhaps unconsciously - researcher degrees of freedom until p<.05" Alternatively: "Manipulation of statistics such that the desired outcome assumes "statistical significance", usually for the benefit of the study's sponsors" [7].
• A recent study of abstracts between 1990-2015 showed 96% contained at least 1 p value < 0.05.  Are we that wildly successful in research? Or, are statistically nonsignificant results published less frequently (probably).  Or, do we try to find something in the data to report as significant, i.e. p-hack (likely).

P values are neither good nor bad. They serve a role that we have distorted and, according to the American Statistical Association: The widespread use of “statistical significance” (generally interpreted as “p ≤ 0.05”) as a license for making a claim of a scientific finding (or implied truth) leads to considerable distortion of the scientific process [1].  In sum, acknowledge what the p value is and is not and, by all means, do not p alone.

References:

1. Wasserstein RL, Lazar NA. The ASA’s statement on p-values: context, process, and purpose. Am Stat. 2016;1305(April):00–00. doi:10.1080/00031305.2016.1154108.
2. Goodman S. (2008) A dirty dozen: twelve p-value misconceptions. Seminars in hematology, 45(3), 135-40. PMID: 18582619 
3. Fisher RA. Statistical Methods for Research Workers. Edinburgh, United Kingdom: Oliver&Boyd; 1925.
4. Sainani KL. Putting P values in perspective. PM R. 2009;1(9):873–7. doi:10.1016/j.pmrj.2009.07.003.
5. Sellke T, Bayarri MJ, Berger JO.  Calibration of p Values for Testing Precise Null Hypotheses.  The American Statistician, February 2001, Vol. 55, No. 1
6. Chavalarias D, Wallach JD, Li AHT, Ioannidis JPA. Evolution of Reporting P Values in the Biomedical Literature, 1990-2015. Jama. 2016;315(11):1141. doi:10.1001/jama.2016.1952.
7. PProf.  "P-Hacking."  Urban Dictionary. Accessed May 1, 2016.  Available at: http://www.urbandictionary.com/define.php?term=p-hacking