Morphological characterisation of breeds of sheep: A discriminant analysis approach

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In this study the characterisation and separation or discrimination of three sheep breeds (crosses, West African Dwarfs (WAD) and West African Long Legged (WALL) based on their physical traits (morphological characterisation) was investigated extensively with the application of discriminant analysis. The study's main objective was speci cally based on developing a variable selection criterion that can discriminate best among the three sheep breeds as well as obtain a reliable mathematical function or equation (discriminant function) for provision of maximum separation among the three known sheep breeds. Data from College of Education, Mampong animal farms on various breeds of sheep (hybrid/crossed breed, Sahell or WALL and Djallonke or WAD) were used. Factor Analysis was employed as a variable selection criterion for selecting six sheep traits that can discriminate best among the sheep breeds. Canonical discriminant function was derived for the eight variable data set and was compared with the derived Quadratic Discriminant Functions (QDF) using the six extracted sheep traits. The six variable QDF distance classi er provided maximum separation after cross validation than the 8-variable canonical discriminant functions. The derived mathematical functions (QDFs) were able to provide maximum separation among the three known sheep breeds with a correct classi cation rate of 0.86. The study recommended the use of a Quadratic Discriminant Function for discrimination and classi cation of breeds of animal since it gives more accurate results than other classi ers such as Linear Discriminant Function.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fufillment of the requirement for the degree of Master of Philosophy in Mathematical Statistics, 2016