# Statistics for Environmental Engineers

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Let us assume that the best calibration line is to be determined and that the measured concentrations will be accompanied by a statement of their precision. This raises several statistical questions (Miller and Miller, 1984):

1.    Does the plot of the calibration curve appear to be well described by a straight line? If it appears to be curved, what is the mathematical form of the curve?

2.    Bearing in mind that each point on the calibration curve is subject to error, what is the best straight line (or curved line) through these points?

3.    If the calibration curve is actually linear, what are the estimated errors and confidence limits for the slope and intercept of the line?

4.    When the calibration curve is used for the analysis of a test specimen, what are the error and confidence limits for the determined concentration?

The calibration curve is always plotted with the instrument response on the vertical (y) axis and the standard concentrations on the horizontal (x) axis. This is because the standard statistical procedures used to fit a calibration line to the data and to interpret the precision of estimated concentrations assume that the y values contain experimental errors but the x values are error-free. Another assumption implicit in the usual analysis of the calibration data is that the magnitude of the errors in the y values is independent of the analyte concentrations. Common sense and experience indicate that measurement error is often proportional to analyte concentration. This can be checked once data are available and the model has been fitted. If the assumption is violated, fit the calibration curve using weighted least squares as explained in Chapter 37.

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