One way to visualize the internal standard method is to create one calibration curve that doesn't use the method and one calibration curve that does. Suppose there are known concentrations of nickel in a set of calibration solutions: 0 ppm, 1.6 ppm, 3.2 ppm, 4.8 ppm, 6.4 ppm, and 8 ppm. Each solution also has 5 ppm yttrium to act as an internal standard. If these solutions are measured using ICP-OES, the intensity of the yttrium signal should be consistent across all solutions. If not, the intensity of the nickel signal is likely imprecise as well.
The calibration curve that does not use the internal standard method ignores the uncertainty between measurements. The coefficient of determination (R) for this plot is 0.9985.
In the calibration curve that uses the internal standard, the y-axis is the ratio of the nickel signal to the yttrium signal. This ratio is unaffected by uncertainty in the nickel measurements, as it should affect the yttrium measurements in the same way. This results in a higher R, 0.9993.