ABSTRACT. In a hypothesis test, a researcher initially fixes a type I error rate, that is, the probability of rejecting the null hypothesis given that it is true. In the case of means tests, it is important to present a type I error that is equal to the nominal pre-fixed level, such that this error remains unchanged across various scenarios, including the number of treatments, number of repetitions, and coefficient of variation. The purpose of this study is to analyse and compare the following multiple comparison tests for the control of both conditional and unconditional type I error rates, depending on a significant F-test in the analysis of variance: Tukey, Duncan, Fisher’s least significant difference, Student-Newman-Keuls (SNK), and Scheffé. As an application, we present a motivation study and develop a simulation study using the Monte Carlo method for a total of 64 scenarios. In each simulated scenario, we estimate the comparison-wise and experiment-wise error rates, conditional and unconditional on a significant result of the overall F-test of analysis of variance for each of the five multiple comparison tests evaluated. The results indicate that the application of the means tests based only on the significance of the F-test should be considered when determining the error rates, as this can change them. In addition, we find that Fisher’s test controls for the comparison-wise error rate, the Tukey and SNK tests control for the experiment-wise error rate, and the Duncan and Fisher tests control for the conditional experiment-wise error rate. Scheffé’s test does not control for any of the error rates considered.

Fusarium wilt, caused by Fusarium oxysporum Schlecht. f. phaseoli Kendrick and Snyder (FOP), is a major disease of common bean, causing large economic losses. Genetic resistance is one of the main mechanisms of pathogen control, and knowledge of the physiological variability is fundamental in breeding for resistant cultivars. Thus, a method of pathogen classification that describes the variability and is useful in plant breeding of isolates from different sources was evaluated by different methodologies. Common bean plants of different sets of differentiating cultivars were inoculated with 25 FOP isolates and 3 controls, totaling 28 isolates evaluated 30 days after inoculation. The variability in the isolates found in this study differs from the results of other authors, who reported a small number of physiological races of the pathogen and disagrees with their evaluation of the races and the evaluation methodology. The proposed approach for binary classification based on a group of 12 differentiating cultivars demonstrated that the variability in pathogenicity of FOP is greater than reported so far. By this methodology, 27 different physiological races of the pathogen were obtained. The methods led to contrasting results, with double race classification in the same isolate. The physiological variability found indicates that the physiological races of the pathogen are not limited to 7 as previously mentioned.