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Title: Analysis and Interpretation of Interactions in Agricultural Research

item VARGAS, MATEO - University Of Chapingo
item Glaz, Barry
item ALVARADO, GREGORIO - International Maize & Wheat Improvement Center (CIMMYT)
item PIETRAGALLA, JULIAN - International Maize & Wheat Improvement Center (CIMMYT)
item MORGOUNOV, ALEXEY - International Maize & Wheat Improvement Center (CIMMYT)
item ZELENSKIY, YURIY - International Maize & Wheat Improvement Center (CIMMYT)
item CROSSA, JOSE - International Maize & Wheat Improvement Center (CIMMYT)

Submitted to: Agronomy Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 3/12/2014
Publication Date: 7/14/2014
Citation: Vargas, M., Glaz, B.S., Alvarado, G., Pietragalla, J., Morgounov, A., Zelenskiy, Y., Crossa, J. 2014. Analysis and Interpretation of Interactions in Agricultural Research. Agronomy Journal. 10:2134.

Interpretive Summary: At its 2011 meeting, the Editorial Board of the Agronomy Journal determined that there were a large number of manuscripts submitted to the Journal that reported on well designed and well conducted studies. However, many of these manuscripts were rejected for publication due to improper statistical analyses and/or poor interpretations of statistical analyses. Therefore, the Editorial Board developed a Statistical Series of invited articles for the Journal. The Series would report on basic principles of statistics and commonly used statistical procedures. Authors were asked to write their invited manuscripts as teaching articles for biological scientists rather than as scholarly articles for fellow statisticians. One of the major faults cited by the Editorial Board was that authors were doing an excellent job of designing meaningful interactions into their experiments, but then ignoring the analysis and interpretation of these interactions in their manuscripts. The purpose of our article was to provide guidance to biological scientists on analyzing and interpreting interactions involving fixed effects. Distinguishing between random and fixed effects is discussed in other articles in this Series, but quickly we will use a common example to describe a fixed effect. When a breeder has advanced 10 genotypes after years of selection and plants a repeated set of replicated trials with only those 10 genotypes, then genotype is a fixed effect. The breeder will be interested in making inferences only about those 10 genotypes from this set of repeated and replicated trials. Our article used data with four fixed effects and stepped the reader through a series of scenarios, beginning with ignoring interactions and finishing with properly analyzing and interpreting the complete set of interactions. We provided analysis of variance results, a macro containing SAS code that researchers can use to calculate single degree of freedom interactions, and explanations and interpretations of significant interactions which included graphs to help in these explanations and interpretations. We showed that results and conclusions changed substantially step by step as each new level of interaction was added to the analysis until we reached the full and proper analysis. In summary, we used real data as an example to show how to analyze and interpret interactions. Then, through our step by step procedure, we illustrated to biological researchers that by ignoring interactions, they would probably not discover all of the important information that was actually uncovered by their well-designed research. Thus, our article teaches researchers how to analyze and interpret interactions and why it is crucial for them to do so properly in order to extract and report the most useful information possible from their research.

Technical Abstract: When reporting on well conducted research, a characteristic of a complete and proper manuscript is one that includes analyses and interpretations of all interactions. The purpose of this article is to provide specific guidelines on how to analyze and interpret interactions of fixed effects in research which is well designed to include crucial interactions. We used a data set with four fixed factors and stepped through an analysis by first ignoring interaction, and then adding in two-way, three-way, and four-way interactions one step at a time. We intentionally used this incorrect procedure as a tool to illustrate that it is crucial to include all interactions in an analysis. We followed this by stepping through the analysis appropriately, that is, by starting with the highest order (four-way) interaction and working down through the lower-order interactions to ensure that all important interactions were covered. Researchers must analyze all interactions, determine if they are due to changes in rank (crossover) or due only to changes in scale, and then judge if reporting on the significant main effects or interactions would best explain the biological responses in their experiments. For an experiment with more than one factor, complete and correct analysis of interactions is essential in order to report on and interpret the research properly.