Statistical Approaches in Analysis of Variance: from Random Arrangements to Latin Square Experimental Design

Background: The choices of experimental design as well as of statistical analysis are of huge importance in field experiments. These are necessary to be correctly in order to obtain the best possible precision of the results. The random arrangements, randomized blocks and Latin square designs were reviewed and analyzed from the statistical perspective of error analysis. Material and Method: Random arrangements, randomized block and Latin squares experimental designs were used as field experiments. A series of previously published data were analyzed. An algorithm for errors analysis was developed and applied on the experimental data. Results: The analysis revealed that the errors classification in random arrangements is: Error(Treatment) < Error(Total) < Error(Experiment). The errors classification in randomized blocks revealed to be: Error(Treatment) < Error(Total) < Error(Experiment) < Error(Block). The obtained errors classification in Latin square was as follows: Error(Experiment) < Error(Treatment) < Error(Total) < Error(Column) < Error(Row). Conclusions: The Latin square design proved to have the smallest experimental errors

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