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

Leonardo Journal of Sciences. 2009;8(15):71-82


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Journal Title: Leonardo Journal of Sciences

ISSN: 1583-0233 (Print)

Publisher: AcademicDirect

LCC Subject Category: Science: Science (General)

Country of publisher: Romania

Language of fulltext: English

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Time From Submission to Publication: 21 weeks


Abstract | Full Text

Background: The choices of experimental design as well as of statisticalanalysis are of huge importance in field experiments. These are necessary tobe correctly in order to obtain the best possible precision of the results. Therandom arrangements, randomized blocks and Latin square designs werereviewed and analyzed from the statistical perspective of error analysis.Material and Method: Random arrangements, randomized block and Latinsquares experimental designs were used as field experiments. A series ofpreviously published data were analyzed. An algorithm for errors analysis wasdeveloped and applied on the experimental data. Results: The analysisrevealed that the errors classification in random arrangements is:Error(Treatment) < Error(Total) < Error(Experiment). The errorsclassification in randomized blocks revealed to be: Error(Treatment) <Error(Total) < Error(Experiment) < Error(Block). The obtained errorsclassification 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 compared to randomized arrangement and randomized block design. Theclassification of errors proved to be similar in randomized arrangements andrandomized block design.