Adding and Subtracting Percentiles — How bad can it be?

When performing anthropometric analysis or design, it frequently happens that some particular anthropometric value is not tabulated although it would appear to be derivable by adding or subtracting two relevant and tabulated dimensions. Because percentile values are usually required, there is the temptation to add or subtract the relevant percentile values of the two tabulated dimensions. In some cases, this will produce minimal or no error between the actual percentile value and the result of adding/subtracting the tabulated values, while in other cases, the resulting percentile will be very seriously in error. The magnitude of the errors depends on the percentiles, correlation coefficient and ratio of the standard deviations of the two variates.

This paper details the combinations of these three factors for which adding/subtracting two identical percentile values produces acceptable as well as grossly misleading results. Several tables, charts and equations are provided to aid in this common problem. The results may be particularly useful when only the ratio of standard deviations may be known or approximated rather than their individual values. In general, subtracting percentiles leads to greater errors than adding them.