LAUSR

In this study, 2 different methods for determining strictly conservative confidence intervals for expected values in the case of heteroscedastic errors are presented. A conservative confidence interval means that a given false positive error rate is not exceeded. The novelty in both approaches is in carrying out the required approximations in such a way that this property holds. The other method is based on variance stabilizing transformations and given as 2 variants, Transformation Models I and II. For variant II, a rigorous proof is given to show that a given false positive error rate is not exceeded if the underlying distributional assumptions are valid. The second method is based on modeling the variance as a function of the expected value, and this is also given as 2 variants, Variance Models I and II. In all cases, only random errors are considered. The methods were tested and compared by applying them to a real case of breath alcohol concentration measurements performed by the Finnish law enforcement authorities, and also by simulation studies. The methods compared were studied by simulating a sample that had the same distributional properties as the real data. These studies showed that Variance Model I is overly conservative, and Variance Model II doesn't quite satisfy the set rate. Both transformation models give too many false positives at concentrations levels exceeding the prosecution limits, but in the range of prosecution limits they could be used.