International Journal of Modern Mathematics
c©2008 Dixie W Publishing Corporation, U. S. A.
Effects of Sample Size Ratio on the Performance of the Linear
Department of Statistics, University of Agriculture, Abeokuta City, 11001, Nigeria
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Health and Social Care Modelling Group, University of Westminster, London W1W 6UW, UK
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Joseph Olutayo Iyaniwura
Department of Statistics, University of Ibadan, Nigeria
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Received March 1, 2007; Revised September 5, 2007
We investigate the performance of the homoscedastic discriminant function (LDF) un-
der the non-optimal condition of unequal group representation (prior probabilities) in
the population and the asymptotic performance of the classification function under this
condition. Results obtained have shown that the misclassification of observations from
the smaller group escalates when the sample size ratio 1:2 is exceeded and this increase
in error rate is not corrected by increasing the sample size. Performance of the function
is observed to be more susceptible to higher variability in the reported error rates.
Keywords: Discriminant function, prior probabilities, misclassification.
2000 Mathematics Subject Classification: 62H30, 62C05, 00A72.