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Stable genotype would not contribute much variation to the variance in productivity over a region. In practice, however, genotypes do usually interact with their environment and show wide variations in stability. Since crop productivity is usually subject to risk, breeders have to exploit the opportunity of genotype by environment interaction which describes how well each genotype will respond to different growing conditions. To analyze such interactions, a number of parametric and nonparametric statistical methods have been developed by different researchers. However, considerable debates of opinion still exist between the leading protagonists of the different statistical methods in identifying the best and most suitable procedure to be used for a specific data set or production environment. This Thesis work, therefore, provides information about the relationship among the various statistical methods. I hope this work will help plant breeders in judging which method will explainbest for a specific data set and whether a genotype is widely or specifically adapted.