R.A. Fisher: An Appreciation pp 161-170 | Cite as

# Discriminant Analysis

## Abstract

Between 1936 and 1940 Fisher published four articles on statistical discriminant analysis, in the first of which [CP 138] he described and applied the linear discriminant function. Prior to Fisher the main emphasis of research in this, area was on measures of difference between populations based on multiple measurements. In this presentation, I shall briefly summarize the early work from Karl Pearson up to Mahalanobis, and then describe the major contributions associated with Fisher. These include the derivation of the linear discriminant function and its relationship to regression in the two-sample case, extensions to s populations for s 003E 2, and a test of significance associated with the linear discriminant function.

## Keywords

Discriminant Analysis Linear Discriminant Analysis Secular Variation Linear Discriminant Function Dispersion Matrix## Preview

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## References and Bibliography

## Early Period

- Pearson, K. (1916). “On the Probability that Two Independent Distributions of Frequency Are Really from the Same Population,” Biometrika, 8, 250–254.CrossRefGoogle Scholar
- Tildesley, M.L. (1921). “A First Study of the Burmese Skull,” Biometrika, 13, 247–251.Google Scholar
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- Hotelling, H. (1931). “The Generalization of Student’s Ratio,” The Annals of Mathematical Statistics, 2, 360–378.zbMATHCrossRefGoogle Scholar
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## Contemporaries of Fisher

- Barnard, M.M. (. 1935 ). “The Secular Variations of Skull Characters in Four Series of Egyptian Skulls,” Annals of Eugenics, 6, 352–371.CrossRefGoogle Scholar
- Bose, S.N. (1936). “On the Complete Moment Coefficients of the D2 Statistic”, Sankhya, 2, 385–396.Google Scholar
- Bose, R.C. (1936). “On the Exact Distribution and Moment Coefficients of the D2- Statistic,” Sankhya, 2, 143–154. Corrected and modified paper: Sankhya, 2, 379–384.Google Scholar
- Martin, E.S. (1936). “A Study of the Egyptian Series of Mandibles with Special Reference to Mathematical Methods of Sexing,” Biometrika., 28, 149–178.Google Scholar
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- Bose, S.N. (1937). “On the Moment-Coefficients of the D2-Statistic, and Certain Integral and Differential Equations Connected with the Multivariate Normal Populations,” Sankhya, 3, 105–124.Google Scholar
- Bose, R.C. and Roy, S.N. (1937). “On the Distribution of Fisher’s Taxonomic Coefficient and Studentised D2-Statistic,” Science and Culture, 3, 335.Google Scholar
- Bose, R.C. and Roy, S.N. (1938). “The Distribution of the Studentised D2-Statistic” Sankhya, 4, 19–38.MathSciNetGoogle Scholar
- Hsu, P.L. (1938). “Notes on Hotellings Generalized T2,” The Annals of Mathematical Statistics, 9, 231–243.zbMATHCrossRefGoogle Scholar
- Bartlett, M.S. (1939). “The Standard Errors of Discriminant Function Coefficients,” Supplement to the Journal of the Royal Statistical Society, 6, 169–173.MathSciNetCrossRefGoogle Scholar
- Girshick, M.A. (1939). “On the Sampling Theory of Roots of Determinantal Equations” The Annals of Mathematical Statistics, 10, 203–224.MathSciNetzbMATHCrossRefGoogle Scholar
- Hsu, P.L. (1939). “On the Distribution of Roots of Certain Determinanta1 Equations” Annals of Eugenics, 9, 250–258.CrossRefGoogle Scholar
- Roy, S.N. (1939). “A Note on the Distribution of the Studentised D2-Statistic,” Sankhya, 4, 373–380.Google Scholar
- Roy, S.N. (1939). “P-Statistics and Some Generalizations in Analysis of Variance,” Sankhya, 4, 381–396.Google Scholar
- Welch, B.L. (1939). “Note on Discriminant Functions,” Biometrika, 31, 218–220.MathSciNetzbMATHGoogle Scholar
- Roy, S.N. and Bose, R.C. (1940). “The Use and Distribution of the Studentised D2-Statistic when the Variances and Covariances are Based on Samples,” Sankhya, 4, 535–542.MathSciNetGoogle Scholar
- Bhattacharya, D.P. and Narayan, R.D. (1941). “Moments of the D2-Statistic for Populations with Unequal Dispersions,” Sankhya, 5, 401–412.MathSciNetGoogle Scholar
- Goodwin, C.N. and Morant, G.M. (1941). “The Human Remains of Iron Age and Other Periods from Maiden Castle, Dorset,” Biometrika, 31, 295–312.Google Scholar
- Wald, A. (1944). “On a Statistical Problem Arising in the Classification of an Individual into One of Two Groups,” The Annals of Mathematical Statistics, 15, 145–162.MathSciNetzbMATHCrossRefGoogle Scholar
- Von Mises, R. (1954). “On the Classification of Observation Data into Distinct Groups,” The Annals of Mathematical Statistics, 16, 68–73.CrossRefGoogle Scholar

## Recent References

- Cacoullos, T. and Styan, G.P.A. (1973). “A Bibliography of Discriminant Analysis,” in Discriminant Analysis and Applications edited by T. Cacoullos. New York: Academic Press.Google Scholar
- Das Gupta, S. (1973). “Theories and Methods in Classification: A Review,” in Discriminant Analysis and Applications edited by T. Cacoullos. New York: Academic Press.Google Scholar
- Rao, C.R. (1973). Linear Statistical Inference and Its Applications. 2nd edition. New York: John Wiley and Sons. [Discussion of discriminant analysis and classification in Chapter 8].zbMATHCrossRefGoogle Scholar