Discrimination of DNA ploidy patterns by order statistics.
The use of order statistics to discriminate and classify DNA ploidy patterns is proposed, especially for the classification of additional observations: whether a given sample is more likely to have come from a normal or an abnormal tissue, and with what probability, based on its ploidy pattern. The method involves the order of observations within each of several samples (e.g., euploid and aneuploid DNA patterns) and the use of subsets of the obtained order statistics as independent variables in a linear discriminant analysis. It thus replaces univariate observations by (some of) their order statistics, which are then used as the variables in the discriminant analysis. The procedure does not require normality of distributions or the transformation of nonnormal distributions, as do many discriminant functions; order statistics are usually distribution-free and thus are particularly useful for nonparametric inference. Preliminary simulation studies verified the potential usefulness of the order statistics discriminant function method as applied to DNA ploidy analysis. Its advantages as compared to the usual methods for hypothesis testing, e.g., the use of the chi-square or Kolmogorov-Smirnov tests to as certain "goodness-of-fit," is discussed. The proposed method is easy to implement and easy to interpret; it is also applicable to the study of distributions of other types of measurements.