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.