# Statistical Rounding and the (Mis)Leading Zero

Sometimes editors (not you or I, of course) obey the rules of their institution’s preferred style manual without fully understanding, or really thinking about, why some of these rules exist. For example, some editors (not you or I, of course) automatically delete (or, if they’re lucky, their editing program deletes for them) the leading zero in a few statistics, but not all. They know exactly when and where to delete the leading zero, but not why. Or they round some statistics, but not all, assuming that all of this has something to do with saving space. It does, of course,1(p830) but this isn’t the only reason we do it.

The AMA Manual of Style defines a P value as “The probability of obtaining the observed data (or data that are more extreme) if the null hypothesis were exactly true.”1(p888) Per AMA style, P values greater than .01 are expressed to a maximum of 2 decimal places and those less than .01 are expressed to a maximum of 3 decimal places. I set out in search of the complicated statistical reason why we use this specific number of decimal places and found that, in addition to saving space, we do it for one simple reason: it’s all we need. Yep, that’s it. It’s all we need to know. P < .00000001 doesn’t tell us any more of value than P < .001. Both tell us that the probability is very low, and that’s good enough. Of course, if the author protests or rounding will make P appear nonsignificant, an exception is made (for example, if P = .046 and significance is set at P = .05).1(pp851-852) Also, studies such as genome-wide association studies report P values of P < .00001 or smaller, often in scientific notation, to address the issue of multiple comparisons; it is essential not to round these. So every rule has exceptions, I guess (remember Spanish class, anyone?).

Why then, you ask, do we not save ourselves the confusion and simply round P < .001 to P = .00? There’s a reason for that, too, and it’s the same reason we don’t use leading zeros with certain probability statistics (ah, you say, it all comes together). If probability is the chance that a given event will occur,2 and we have only surveyed a sample of a given population, probability cannot equal 1.0 or 0 because we can’t say absolutely that a null hypothesis will definitely or definitely not happen in that population.1(p889) And if P can’t equal 1.0 or 0, why include a zero that doesn’t tell us anything new? For this reason, we use P > .99 and P < .001 as the highest and lowest P values. For the same reason, and because they are used often, the leading zero rule applies to α and β probabilities as well. Why? To save space, of course.–Roya Khatiblou, MA

1. Iverson C, Christiansen S, Flanagin A, et al. AMA Manual of Style: A Guide for Authors and Editors. 10th ed. New York, NY: Oxford University Press; 2007.

2. Merriam-Webster’s Collegiate Dictionary. 10th ed. Springfield, MA: Merriam-Webster Inc; 1997.

## 2 thoughts on “Statistical Rounding and the (Mis)Leading Zero”

1. Mary Nishikawa, Medical Tribune, Inc. Japan

It is useful for journal editors to know why the AMA Manual of Style recommends the omission of leading zeros for P values and α and β probabilities. Please place this information in the next edition of the manual. Thanks!

• This is addressed in section 19.7.1 of the Manual. Thanks!