Setting number of decimal places for reporting risk ratios: rule of four.

Precision and rounding—decimal places and significant digits Reporting of numerical data is an important element in medical research. Summary statistics are often reported to too many decimal places, leading to spurious precision and over-complicated presentation1; less often, too few decimal places are used, resulting in a lack of precision. Surprisingly, few guidelines on the subject exist. The SAMPL (Statistical Analyses and Methods in the Published Literature) guidelines on the EQUATOR Network repository (http://equator-network.org) say: “Report numbers . . . with an appropriate degree of precision. For ease of comprehension and simplicity, round to a reasonable extent.”2 One might call this the Goldilocks rounding principle—not too little, not too much. The EASE guidelines state that in tables “numbers should be given in (sic) 2-3 effective digits,”3 and APA Style requires consistently one or two decimal places.4 Precision is controlled by the degree of rounding used, expressed in terms of decimal places or significant figures. (Here the phrase significant digits is used in preference to significant figures or effective digits; note that it has nothing to do with statistical significance.) The number of decimal places is the number of digits that appear after the decimal point, whereas the number of significant digits is the total number of digits, ignoring the decimal point (and ignoring any leading zeros). Trailing zeros are assumed to be informative, not just placeholders, except in special cases (see “significant figures” in Wikipedia for a full explanation). The number 1.2345 has four decimal places and five significant digits, whereas 123.45 has two decimal places and five significant digits. Shifting the decimal point affects the decimal places but not the significant digits, so significant digits are generally more flexible than decimal places. Rounding inevitably introduces error; rounded to two decimal places 1.2345 becomes 1.23, so the rounding error is 0.0045. With two decimal places, the maximum possible rounding error is 0.005; this is so because, as 1.23 is rounded, the unrounded number must be closer to 1.23 than to 1.22 or 1.24—that is, lying between 1.225 and 1.235—giving an error of up to 0.005 on either side.