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Data generated from the designed experiments is analyzed under certain assumptions. If any of these assumptions is violated, the conclusion drawn from this analysis may be false. For example, like many other fields data obtained from designed experiments is analyzed assuming that the error distribution of observations is normal and homogeneous. These assumptions are frequently violated in practice. In general many examples of such kind could be quoted in linear regression models. But in particular, it is also a common phenomenon in case of designed experiments. It is very difficult to analyze data under non-normal and heterogeneous set-up. There are two major ways in which the outliers can be handled. One way of handling outliers is the development of diagnostic tools (identification) and the other is robust regression (accommodation). The book deals with the development of robust methods of analysis of experimental design and their application in some real experimental data set obtained from the Agricultural Field Experiments Information System (AFEIS), IASRI. New Delhi. M-estimation method is discussed in detail and it is used for analyzing agricultural field experiments data.