Date of Award:
Master of Science (MS)
Mathematics and Statistics
Neeti R. Bohidar
The analysis of variance technique is probably the most popular statistical technique used for testing hypotheses and estimating parameters. Eisenhart presents two classes of problems solvable by the analysis of variance and the assumption underlying each class. Cochran lists the assumptions and also discusses the consequences when these assumptions are not met. It is evident that if all the assumptions are not satisfied, the confidence placed in any result obtained in this manner is adversely affected to varying degrees according to the extent of the violation. One of the assumptions in the analysis of variance procedures is that of uncorrelated errors. The experimenter may not always meet this conditions because of economical or environmental reasons. In fact, Wilk questions the validity of the assumption of uncorrelated errors in any physical situation. For example, consider an experiment over a sequence of years. A correlation due to years may exist, no matter what randomization technique is used, because the outcome of the previous year determines to a great extent the outcome of this year. Another example would be the case of selecting experimental units from the same source, such as, sampling students with the same background or selecting units from the same production process. This points out the fact that the condition such as background, or a defect in the production process may have forced a correlation among the experimental units. Problems of this nature frequently occur in Industrial, Biological, and Psychological experiments.
Chang, Tseng-Chi, "Error Structure of Randomized Design Under Background Correlation with a Missing Value" (1965). All Graduate Theses and Dissertations. 6818.
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