Analyzing one-way experiments: a piece of cake of a pain in the neck?

Abstract

Statistics may be intricate. In practical data analysis many researchers stick to the most common methods, not even trying to find out whether these methods are appropriate for their data and whether other methods might be more useful. In this paper I attempt to show that when analyzing even simple one-way factorial experiments, a lot of issues need to be considered. A classical method to analyze such data is the analysis of variance, quite likely the most often used statistical method in agricultural, biological, ecological and environmental studies. I suspect this is why this method is quite often applied inappropriately: since the method is that common, it does not require too much consideration-this is how some may think. An incorrect analysis may provide false interpretation and conclusions, so one should pay careful attention to which approach to use in the analysis. I do not mean that one should apply difficult or complex statistics; I rather mean that one should apply a correct method that offers what one needs. So, various problems concerned with the analysis of variance and other approaches to analyze such data are discussed in the paper, including checking within-group normality and homocedasticity, analyzing experiments when any of these assumptions is violated, outliers presence, multiple comparison procedures, and other issues. Key words: analysis of variance, assumptions, graphical statistics, multiple comparisons, normal distribution, non-parametric statistics, one-way designs, statistical analysis ANÁLISE ESTATÍSTICA DE EXPERIMENTOS COM UM ÚNICO FATOR: MUITO FÁCIL OU MUITO DIFÍCIL?Resumo: Realizar análises estatísticas pode ser complicado. Em situações práticas muitos pesquisadores utilizam os procedimentos de análise mais comuns, sem investigar se os mesmos são apropriados para os seus resultados, ou mesmo se há outros métodos que poderiam ser mais adequados. Nesse artigo buscarei mostrar que mesmo na análise de experimentos de classificação simples (com um único fator) vários aspectos precisam ser considerados. A forma clássica de análise desse tipo de dados é a análise de variância, que é provavelmente o método estatístico mais usado na agricultura, biologia, ecologia e estudos de meio ambiente. Suspeito que essa é a razão pela qual tal método é frequentemente usado de forma inapropriada: uma vez que ele é muito usado, não suscita maiores considerações. Imagino que seja esse raciocínio que muitos pesquisadores devam empregar. Análises incorretas podem fornecer falsas interpretações e conclusões, e dessa forma é importante prestar atenção na escolha do procedimento a ser usado na análise. Não estou sugerindo que algum método difícil ou complexo deva ser usado, mas sim que um método correto seja adotado, de forma a fornecer os resultados adequados. Dessa forma, vários problemas relacionados à análise de variância e outras abordagens para analisar esse tipo de dados são discutidas nesse artigo, incluindo verificações de normalidade e homogeneidade de variâncias, análise de experimentos...

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