Discrimination analysis in medicine.

Radhakrishna, S.

The Statistician; 1964; 14; 147-167.

The technique of discrimination analysis between two groups was first suggested by Fisher (1936) to distinguish between two species of iris flowers, setosa and versicolor. The data available in this instance were measurements (x i ) of sepal length, sepal width, petal length and petal width from 50 flowers of each type. Fisher suggested the construction of a new variable y, which would be a linear combination of the measurements x i , such that the ratio of the difference between the mean values of y for the two species to its standard error would be maximised. For any other flower belonging to the one or the other species, the value of y would be calculated and the flower assigned to the species with the nearer mean value for y. Although originally an empirical approach, this method is now known to be the best in that it results in the minimum chance of misclassification, which is the same for individuals from both populations (see Welch, 1939; Smith, 1947), provided that - (1) the variates x i follow a multinormal distribution and (2) the covariance matrices of the variates (x i ) are the same for both populations.

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