﻿ ﻿Significant Digits and Rounding Numbers - Study Design and Statistics

# Significant Digits and Rounding NumbersStudy Design and Statistics

When numbers are expressed in scientific and biomedical articles, they should reflect the degree of accuracy of the original measurement. Numbers obtained from mathematical calculations should be rounded to reflect the original degree of precision.

19.4.1 Significant Digits.

The use of a numeral in a numbers column (eg, the ones column, the tens column) implies that the method of measurement is accurate to that level of precision. For example, when a reporter attempts to estimate the size of a crowd, the estimate might be to the nearest tens of number of people but would not be expressed as an exact number, such as 86, unless each individual was counted. Similarly, when an author provides a number with numerals to the right of the decimal point, the numerals imply that the measurement used to obtain the number is accurate to the last place a numeral is shown. Therefore, numbers should be rounded to reflect the precision of the instrument or measurement; for example, for a scale accurate to 0.1 kg, a weight should be expressed as 75.2 kg, not 75.23 kg. Similarly, the instrument used to measure a concentration is accurate only to a given fraction of the concentration, for example, 15.6 mg/L, not 15.638 mg/L (see Table 17.5-2 in 17.5.10, Laboratory Values, for the appropriate number of significant digits). Numbers that result from calculations, such as means and SDs, should be expressed to no more than 1 significant digit beyond the accuracy of the instrument. Thus, the mean (SD) of weights of individuals weighed on a scale accurate to 0.1 kg should be expressed as 62.45 (4.13) kg. Adult age is reported rounded to 1-year increments (eg, 52 years), so the mean could be expressed as, for example, 47.7 years.

Odds ratios, risk ratios, hazard ratios, and 95% CIs should have significant digits extending to the one hundredths place (eg, 1.01, 5.26, 9.85, 0.15). Numbers extending beyond the one hundredth place should be rounded.

19.4.2 Rounding.

The digits to the right of the last significant digit are rounded up or down. If the digit to the right of the last significant digit is less than 5, the last significant digit is not changed. If the digit is greater than 5, the last significant digit is rounded up to the next higher digit. (For example, 47.746 years is rounded to 47.7 years and 47.763 years is rounded to 47.8 years.) If the digit immediately to the right of the last significant digit is 5, with either no digits or all zeros after the 5, the last significant digit is rounded up if it is odd and not changed if it is even. For example, 47.7500 would become 47.8; 47.65 would become 47.6. If the digit to the right of the last significant digit is 5 followed by any number other than 0, the last significant digit is rounded up (47.6501 would become 47.7).

P values and other statistical expressions raise particular issues about rounding. For more information about how and why to round P values and other statistical terms, see P value in 19.5, Glossary of Statistical Terms. Briefly, P values should be expressed to 2 digits to the right of the decimal point (regardless of whether the P value is significant), unless P < .01, in which case the P value should be expressed to 3 digits to the right of the decimal point. (One exception to this rule is when rounding P from 3 digits to 2 digits would result in P appearing nonsignificant, such as P  =  .046. In this case, expressing the P value to 3 places is preferred. The same holds true for rounding CIs that are significant before rounding but nonsignificant after rounding.) The smallest P value that should be expressed is P <.001 because additional zeros do not convey useful information.92 P values are expressed without a 0 preceding the decimal point.

P values may be expressed to more than 3 decimal places in genome-wide association and other genetics studies (eg, P = 1 × 10−5), studies that involve the Bonferroni correction (eg, A Bonferroni-corrected significance threshold of .0083 was used to account for . . . ), and other types of studies with adjustments for multiple comparisons, and when the level of significance in a study is defined as a small number much less than P < .05.

P values should never be rounded up to 1.0 or down to 0; rather, the P value should be expressed as P > .99 or P < .001, respectively. Although such a procedure might be justified arithmetically, the results are misleading. P values may approach infinitely close to these upper and lower bounds but never close enough to establish that the associated observation was absolutely predestined (P  =  1.0) or absolutely impossible (P  =  0) to occur because the value represents a probability.