Common statistical mistakes in entomology: models inconsistent with the experimental design

Authors: Spurgeon, Dale

Submitted to: American Entomologist
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 4/22/2019
Publication Date: 6/7/2019
Citation: Spurgeon, D.W. 2019. Common statistical mistakes in entomology: models inconsistent with the experimental design. American Entomologist. 65(2):87-89.

Interpretive Summary: Valid inference from an analysis of variance (ANOVA) requires the analytical model to faithfully represent the experimental design. It is common in the entomological literature that analyses are simplified by excluding structural parts of the experiment, such as blocks or strata, or by analyzing multifactor experiments as multiple, one-way ANOVAs. When the ANOVA model does not represent the physical design of the experiment, the variation associated with the excluded effects does not go away. Instead this variation is absorbed by other effects in the analysis. As a result, the validity of tests of the experimental treatments is compromised and the appropriateness of any conclusions is uncertain. This problem can be avoided by dividing the experimental design into two components: the treatment structure and the design structure. The treatment structure contains the treatments of interest to the investigator, and any interactions between or among treatments. The design structure represents the physical layout of the experiment, including plots, blocks, and replicates of the treatments. Separation of the experimental design into respective treatment and design structures simplifies construction of an ANOVA model that accurately represents the experiment. This simple approach will allow scientists to recognize and correct problems with inaccurate analytical models, and readers to recognize when reported results are not supported by valid tests.

Technical Abstract: Valid inference from an analysis of variance (ANOVA) requires the analytical model to faithfully represent the experimental design. It is common in the entomological literature that analyses are simplified by excluding structural parts of the experiment, such as blocks or strata, or by analyzing multifactor experiments as multiple, one-way ANOVAs. When the ANOVA model does not represent the physical design of the experiment, the variation associated with the excluded effects does not go away. Instead this variation is absorbed by other effects in the analysis. As a result, the validity of tests of the experimental treatments is compromised and the appropriateness of any conclusions is uncertain. This problem can be avoided by dividing the experimental design into two components: the treatment structure and the design structure. The treatment structure contains the treatments of interest to the investigator, and any interactions between or among treatments. The design structure represents the physical layout of the experiment, including plots, blocks, and replicates of the treatments. Separation of the experimental design into respective treatment and design structures simplifies construction of an ANOVA model that accurately represents the experiment. This simple approach will allow scientists to recognize and correct problems with inaccurate analytical models, and readers to recognize when reported results are not supported by valid tests.