Beyond Zar: the use and abuse of classification statistics for otolith chemistry.

Classification method performance was evaluated using otolith chemistry of juvenile Atlantic menhaden Brevoortia tyrannus when assumptions of data normality were met and were violated. Four methods were tested [linear discriminant function analysis (LDFA), quadratic discriminant function analysis (QDFA), random forest (RF) and artificial neural networks (ANN)] using computer simulation to determine their performance when variable-group means ranged from small to large and their performance under conditions of typical skewness to double the amount of skewness typically observed. Using the kappa index, the parametric methods performed best after applying appropriate data transformation, gaining 2% better performance with LDFA performing slightly better than QDFA. RF performed as well as QDFA and showed no difference in performance between raw and transformed data while the performance of ANN was the poorest and worse with raw data. All methods performed well when group differences were large, but parametric methods outperformed machine-learning methods. When data were skewed the performance of all methods declined and worsened with greater skewness, but RF performed consistently as well or better than the other methods in the presence of skewness. The parametric methods were found to be more powerful when assumptions of normality can be met and can be used confidently when skewness and kurtosis are minimized. When these assumptions cannot be minimized, then machine-algorithm methods should also be tried.