Can we use discriminant function analysis to sex penguins prior to calculating an index of a morphometric parameter?

In sexually dimorphic species, morphometric parameters have separate distributions for males and females, and these often overlap. Whilst discriminant analysis can be used to determine the sex of individuals, it is only able to correctly sex a certain proportion of birds. Two overlapping normal distributions are used to show that there is a difference between the real mean parameter for a sex, and the apparent mean derived by sexing the birds using discriminant analysis.
When discriminant functions are able to correctly determine the sex of birds with greater than 80% success the difference between the true and apparent mean is likely to be undetectable when fewer than 600 birds are sampled. Combining all data for both sexes is considered as a procedure for avoiding the necessity of sex determination, but uncertainty in sex ratios can lead to considerable Type I and Type II errors. Lack of knowledge about the sex ratio between years makes combining the data a very doubtful procedure and use of a discriminant function to determine sex is recommended as being most practically robust.