How to use the standard addition method calculator
- List each spiked sample with the concentration you added and the signal you measured. Include the unspiked sample with an added amount of 0.
- Use at least three samples with at least two different added amounts.
- If you diluted the sample before measuring, enter the dilution factor so the answer is in the original sample.
- Choose a confidence level and read the unknown concentration, the fitted line, R squared, the standard error and an interval.
Formula
Fit signal = intercept + slope x added by least squares
Unknown concentration = intercept / slope, the distance from the line's zero crossing to zero added
Standard error = (s / |slope|) x sqrt(1 / n + mean signal^2 / (slope^2 x Sxx)), with s the standard deviation of the residuals
Interval = unknown plus or minus t x standard error, with t for n - 2 degrees of freedom
The line is extended backwards to the point where the signal is zero. The distance from there to the origin is the concentration of the sample itself.
A perfect line and a noisy one
Signals of 10, 20 and 30 for added amounts of 0, 1 and 2 lie exactly on a line with slope 10 and intercept 10. The line reaches zero signal at an added amount of -1, so the unknown is 1, with no uncertainty because the fit is perfect.
Added amounts of 0, 2, 4 and 6 with signals of 0.212, 0.318, 0.431 and 0.527 give a slope of 0.0529, an intercept of 0.2133 and R squared of 0.99904. The unknown is 4.0321 with a standard error of 0.16177, so the 95 percent interval is 3.3361 to 4.7282, using a t value of 4.3027 for 2 degrees of freedom. A series of 1.20, 2.31, 3.42 and 4.50 for 0, 5, 10 and 15 added, from a sample that was diluted 10 times, gives 54.768 after the dilution factor is applied.
Why use standard addition
When the sample itself changes how strongly an analyte responds, a calibration made in clean solvent gives the wrong answer. Adding known amounts of the analyte to portions of the sample itself puts every standard in the same matrix, so the slope already includes the matrix effect. The method is common in atomic spectroscopy, electrochemistry and chromatography.
To find the smallest amount your method can detect, see the LOD and LOQ calculator. For fitting a line with more statistics, use the linear regression calculator.
Getting a good result
Spread the added amounts so the largest is a few times the unknown, and keep the total volume the same in every portion, or correct for the change. Because the answer comes from extending the line backwards, a poor fit or a curved response can make it unreliable. Always check that R squared is close to 1 and that the signal does not level off at the top.
More points make the interval narrower. With three points the interval is very wide, which the t value of 12.7 for one degree of freedom reflects. If you diluted the sample first, plan it with the solution dilution calculator.
Assumptions and limits
- The signal is linear in concentration over the range, including below the first point.
- The spiked standards behave like the analyte in the sample, and the volume is the same in every portion.
- The residuals are roughly normal with a constant spread, which the interval needs.
- The extrapolated crossing must lie at or below zero added. Otherwise the page reports a problem.
Frequently asked questions
What is the standard addition method?
It is a way to find an unknown concentration by adding known amounts of the analyte to portions of the sample and extending the line of signal against added amount back to zero signal.
When should I use it?
Use it when the sample matrix changes the response, so a calibration made in clean solvent would not apply.
How many spikes do I need?
At least three samples. Four or five give a much narrower interval than three.
What does the dilution factor do?
It multiplies the answer, so the result is the concentration in the original sample and not in the diluted one.