In family studies, canonical discriminant analysis can be used to find linear combinations of phenotypes that exhibit high ratios of between-family to within-family variabilities. But with large numbers of phenotypes, canonical discriminant analysis may over-fit. To estimate the predicted ratios associated with the coefficients obtained from canonical discriminant analysis, two methods are developed; one is based on bias correction and the other based on cross-validation. Because the cross-validation is computationally intensive, an approximation to the cross-validation is also developed. Furthermore, these methods can be applied to perform variable selection in canonical discriminant analysis.