P values in Medical Writing

#1
My apology for this simple question but it's one I have run into before and would like some assistance with. The following was posted on a medical writing forum to which I subscribe: "I’m working on a paper with exact P values to the 10th decimal place or more (for example, P = 1.7 x 10[-14]). My first inclination was to follow the AMA Manual of Style and ask for no more than 3 significant digits. However, the authors say that they need to use the large number of significant digits because exact values are required for meta-analyses."

As with this writer I am also used to reporting p values with no more than 3 significant digits but I have seen them reported to much higher levels as the writer described. Can someone explain to me in what situations this additional level of detail might be necessary?

Thanks
 
#2
I think that there may be some confusion between decimal places and significant digits.

1.7 x 10E-14 only has two significant digits (the "1" and the "7"), but it has 15decimal places. So you can follow your AMA Manual of Style and still accept the P-value as stated.

i.e., 1.73456 x 10E-14 would represent 6 significant digits and, according to your manual, you would need to round that to 1.73 x 10E-14.
 
#3
Thanks. I think I kind of get it now. The AMA instructions state the "Expressing P to more than 3 significant digits does not add useful information to P < .001, since precise P values with extreme results are sensitive to biases or departures from the statistical model [Bailar JC & Mostellar F. Medical Uses of Statistics. 2nd ed. Boston, MA: NEJM Books; 1992] Re-reading their instructions it now seems to me that the smallest P value they feel is useful is P < .001 anything else is considered extreme. So even though 1.7 x 10E-14 meets the significant digits test it does not meet the decimal place test so they would want me to use p < .001 and leave it at that. I assume that, other than in medicine (or perhaps even in some areas of medicine) this limitation does not apply.
 

Outlier

TS Contributor
#4
meta analysis

"Chaos theory is a field of study in mathematics, physics, and philosophy studying the behavior of dynamical systems that are highly sensitive to initial conditions. This sensitivity is popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general."