Is, Or Is Not, The Two Great Ends Of Fate: Errors In Agronomic Research

Agronomic research results include Type 1 (alpha) and Type 2 (beta) errors. Results are often reported using a alpha <= 0.05 while beta is ignored. Our objective was to discuss whether a false positive was more serious than a false negative in agronomic research. For comparison, current statistical methods used in Agronomy Journal were tabulated. Most papers used null hypothesis tests with a alpha <= 0.05, reporting results based on the LSD among all treatment pairs. Current practices do not account for the relative costs of false positive vs. false negative errors. A case study from the Washington State Wheat Extension trials was analyzed using mixed models with specific contrasts. While the overall effect for cultivar was significant, the beta error rate for the contrast was 40% and additional replications were needed to increase the power of this contrast. A second case study analyzed trials evaluating wheat (Triticum aestivum L.) resistance to Fusarium crown rot. Optimal alpha and beta error rates were estimated for two to eight replications with the Type1/Type2 error cost ratio set at 1:1 and 1:5. An average error rate (alpha and beta) <= 0.05 could be achieved with four replications when a reduction in the beta error was critical and a errors could be corrected in future experiments. Effective experimental design requires estimation of the acceptable magnitude and cost ratio of false positive and false negative errors and critical effect sizes. To be truly informative, reports of results should include this information plus observed effect sizes and variances.