If you measured the temperature of a liquid, you'd get a single result for temperature. But, if you made multiple measurements across different samples, you'd need a way to generalize and represent them together.
When scientists make repeated measurements of the same quantities, whether it's the temperature of a liquid or how much stress is on a concrete weight, they can use the relative percent difference (RPD) to describes these groups or multiple measurements.
Two Point Relative Percent Difference
You can calculate RPD between two points by first finding the relative difference between two quantities across different measurements or samples. Subtract one measurement from the other and take the absolute value of this difference.
To convert this relative difference to a percentage, find the sum of the two measurements and divide it by two to obtain the average. Then, divide the relative difference by this average to get the RPD.
The overall formula is |(x2 - x1)|/((x2 + x1)/2) for two measurements x1 and x2 of the same sample. The denominator ((x2 + x1)/2 represents the average of the two measurements. Keep in mind the 2 in the denominator denotes that there are two quantities to be averaged, x__1 _and _x2. Note also that the formula gives you a decimal answer so, to convert to percent, multiply it by 100.
As an example problem, imagine that your rent has increased from $900 to $1,000 from one month to the next. The percent relative difference is, then, |(1000-900)|/((900+1000)/2) which equals 0.1052 or 10.52 %.
Three or More Percent Differences
The RPD formula only applies to two measurements. If you wanted to compare differences between three or more measurements, you could find the RPD of each pair of measurements. For three data points A, B and C, you'd find the RPD between A and B, A and C, and B and C.
Running experiments many times can help scientists make sure their data points are more representative of the values that they're designed to measure. It lets researchers detect trends they want to observe. Keeping track of RPD values across all observations gives them a distribution of differences of all their data points from which they could draw conclusions.
If you tested three different genes for expression within a genome and ended up with four different expression values for each of the three genes, you would calculate a RPD for each of the four measurements paired against one another for each of the three genes. This could tell you the relative expression levels of these genes in a way that accounts for all measurements across samples.
Percentage Difference Calculator Online
You can find a percentage difference calculator online. Calculator Soup offers one alongside the formula to explain how the value is calculated. NCalculators has one with more functionality and explanations about the values themselves.
This one calculates the percent change. This can help you compare relative percent difference vs. percent change. If you scroll down on the page, you can find another calculator that deals with percentages of numbers.
Use these calculators and online formula to check your results. You can also use software like Microsoft Excel in keeping track of RPD, especially for cases in which you have many data points that need to be analyzed.
You can use the percent difference formula in Excel by inputting the indices for the columns and rows to be summed, subtracted and averaged. For example, if you wanted to sum up the values in cells A1 and A2 you would type "SUM(A1:A2)" in the cell of interest. Or you can write a single formula for the RPD as "(A1-A2)/(AVERAGE(A1:A2))*100" that uses the AVERAGE function for each pair of points you want to calculate.
About the Author
S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.