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# Rounding

Rounding
Chapter:
Study Design and Statistics
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## 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 20.9, 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 may be preferred by the author. The same holds true for rounding confidence intervals that are significant before rounding but nonsignificant after rounding.) The smallest P value that should be expressed is P <.001, since additional zeros do not convey useful information.37

P values should never be rounded up to 1.0 or down to 0. While such a procedure might be justified arithmetically, the results are misleading. Statistical inference is based on the assumption that events occur in a probabilistic, rather than deterministic, universe. P values may approach infinitely close to these upper and lower bounds, but never close enough to establish that the associated observation was either absolutely predestined (P = 1.0) or absolutely impossible (P = 0) to occur. Thus, very large and very small P values should always be expressed as P > .99 and P < .001, respectively.