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Numbers and Percentages

Stephen J. Lurie

and Margaret A. Winker

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The term percent derives from the Latin per centum, meaning by the hundred, or in, to, or for every hundred. The term percent and the symbol % should be used with specific numbers. Percentage is a more general term for any number or amount that can be stated as a percent. Percentile is defined as the value on a scale of 100 that indicates the percentage of the distribution that is equal to or below it.

Ten percent of the work remained to be done.

Heart disease was present in a small percentage of the participants. (But: Five percent of the participants had heart disease.)

Her body mass index placed her in the 95th percentile of the study group.

Unless otherwise indicated, data in the table are expressed as number (percentage).

Use arabic numerals and the symbol % for specific percentages. The symbol is set closed up to the numeral and is repeated with each number in a series or range of percentages. Include the symbol % with a percentage of zero.

A 5% incidence (95% confidence interval, 1%-9%) was reported.

The prevalence in the populations studied varied from 0% to 20%.

At the beginning of a sentence, spell out both the number and the word percent, even if the percentage is part of a series or range. Often it is preferable to reword the sentence so that a comparison between percentages is more readily apparent.

Twenty percent to 30% of patients reported gastrointestinal symptoms.

Better: The percentage of patients who reported gastrointestinal symptoms ranged from 20% to 30%.

Or: Between 20% and 30% of the patients reported gastrointestinal symptoms.

When referring to a percentage derived from a study sample, include with the percentage the numbers from which the percentage is derived. This is particularly important when the sample size is less than 100 (see also 20.8, Study Design and Statistics, Significant Digits and Rounding Numbers). To give primacy to the original data, it is preferable to place the percentage in parentheses.

Of the 26 adverse events, 19 (73%) occurred in infants.

Any discrepancy in the sum of percentages in a tabulation (eg, due to rounding numbers, missing values, or multiple procedures) should be explained in the text, table footnote, or figure legend.

The terms percent change, percent increase, and percent decrease are often used in place of percentage of change. Although these less formal terms are acceptable, their usage must be precise. They generally are computed as the difference between an index value and either an earlier or later value, divided by the index value. Although a percent increase may exceed 100%, a percent decrease generally cannot. A percent decrease can also be expressed as a negative percent increase.

These terms must be differentiated from percentage point change, increase, or decrease, which are obtained by subtracting one percentage value from another. For example, a change in rate from 20% to 30% can be referred to either as an increase of 10 percentage points, as in “the intervention group improved 10 percentage points,” or as a 50% increase (percent change), as in “The intervention group showed a 50% improvement” ([30%-20%]/20%). The 2 terms are not interchangeable. Since the percent change does not indicate the actual beginning or ending values or the magnitude of the change, the actual values should be provided whenever possible.

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