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

Abstract

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 ( Y C and X C ) and true Currie detection limits ( Y D and X D ) 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 Y C = 56.1 mV, Y D = 125. mV, X C = 0.132 μg /mL and X D = 0.294 μg /mL. For 5% probability of false positives and 1% probability of false negatives, the obtained detection limits were Y D = 158. mV and X D = 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.