True detection limits in an experimental linearly heteroscedastic system. Part 1

Using a lab-constructed laser-excited filter fluorimeter deliberately designed to exhibit linearly heteroscedastic, additive Gaussian noise, it has been shown that accurate estimates may be made of the true theoretical Currie decision levels (YC and XC) and true Currie detection limits (YD and XD) for the detection of rhodamine 6 G tetrafluoroborate in ethanol. The obtained experimental values, for 5% probability of false positives and 5% probability of false negatives, were YC = 56.1 mV, YD = 125. mV, XC = 0.132 μg/mL and XD = 0.294 μg/mL. For 5% probability of false positives and 1% probability of false negatives, the obtained detection limits were YD = 158. mV and XD = 0.372 μg/mL. These decision levels and corresponding detection limits were shown to pass the ultimate test: they resulted in observed probabilities of false positives and false negatives that were statistically equivalent to the a priori specified values.