Percent change
In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared. The comparison is expressed as a ratio and is a unitless number. By multiplying these ratios by 100 they can be expressed as percentages so the terms percentage change, percent(age) difference, or relative percentage difference are also commonly used. The distinction between "change" and "difference" depends on whether or not one of the quantities being compared is considered a standard or reference or starting value. When this occurs, the term relative change (with respect to the reference value) is used and otherwise the term relative difference is preferred. Relative difference is often used as a quantitative indicator of quality assurance and quality control for repeated measurements where the outcomes are expected to be the same. A special case of percent change (relative change expressed as a percentage) called percent error occurs in measuring situations where the reference value is the accepted or actual value (perhaps theoretically determined) and the value being compared to it is experimentally determined (by measurement).
Given two numerical quantities, x and y, their difference, Δ = x − y, can be called their actual difference. When y is a reference value (a theoretical/actual/correct/accepted/optimal/starting, etc. value; the value that x is being compared to) then Δ is called their actual change. When there is no reference value, the sign of Δ has little meaning in the comparison of the two values since it doesn't matter which of the two values is written first, so one often works with | Δ | = | x − y |, the absolute difference instead of Δ, in these situations. Even when there is a reference value, if it doesn't matter whether the compared value is larger or smaller than the reference value, the absolute difference can be considered in place of the actual change.
The absolute difference between two values is not always a good way to compare the numbers. For instance, the absolute difference of 1 between 6 and 5 is more significant than the same absolute difference between 100,000,001 and 100,000,000. We can adjust the comparison to take into account the "size" of the quantities involved, by defining, for positive values of xreference:
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