While there is no standard procedure for objectively testing the fit of calibration equations in analytical chemistry, a test for a higher-order polynomial relationship provides a simple, reliable, and objective test for the linearity or curvature of these calibration equations. For example, if a linear calibration curve is expected, then a regression of detector response on the concentration of analyte and the concentration of analyte squared is used to test the significance of a second-order or quadratic effect. If this quadratic effect is statistically significant, the calibration curve is not linear and one or more systematic errors may need to be corrected. If this quadratic effect is not statistically significant, the calibration curve is linear and additional tests of fit are needed. This sequence of statistical tests is automatically done with a Python program that was developed for this study. Accordingly, the analog signal voltage from a spectrophotometer was converted to a digital signal voltage with a MCP3008 microchip. This digital signal voltage was input to a Raspberry Pi 3 computer and processed with the Python program. The output from this Python program was tested using actual calibrations with actual standard solutions, and simulated calibrations with simulated digital signal voltages. The accuracy of output from this Python program was tested against the output from the Analysis ToolPak of Microsoft Excel® 365, as well as the output from a Vernier Go Direct®SpectroVis® Plus Spectrophotometer, which uses the Vernier Spectral Analysis Application for processing. The Python program accurately determined the order of the polynomial that best fits the calibration data at the 95% confidence level. Then it accurately determined if the y-intercept was statistically equivalent to the origin (0,0) at the 95% confidence level.

Developing software that uses a test for a higher-order polynomial relationship to objectively test the fit of calibration equations in analytical chemistry

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