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I'm baffled by the following statement in the abstract:
In an age where performing a statistical test merely requires clicking a button in a computer programme, it could be argued that what the vast majority of biologists need is not mathematical formulae but simple guidance on which buttons to click.
Of course there are softwares to perform statistical analyses, and they require only to click on buttons (unless, that is, one uses R or similar environments, which are emerging as a new standard). But what would the author reply to the exactly equivalent statement of "In an age where performing high-throughput sequencing merely requires a good set of pipettes, it could be argued that what the vast majority of biologists need is not an understanding of the biochemistry involved but simple guidance on which tips to order"? This argument can be made for any method and any tool, and I'm not sure there is a single situation in which it has value.
I think that in the contrary, the solution is more formal training in biostatistics. Applying a method (ANY method) without understanding it is a surefire way to either mis-use it, or be unable to generalize it. That requires to think about the training of undergrad/graduate students, and (I agree with the authors on this point at least) to present equations in a way that appeals to biologists.
+1 to Timothée Poisot's post - you can't do analysis without understanding what statistics is. Indeed you shouldn't be performing an experiment at all unless you know statistics well. A poorly designed experiment will most likely lead to incorrect results. Poor statistical analysis on a good experiment will also produce incorrect results.
Clicking buttons and not understanding any of the process is not science and should not be promoted.
I agree with Wiles (and also agree more training is needed). Figure 1 is very helpful and as pointed out in the abstract the reality is ~50% of published papers contain statistical errors. The authors are trying to address this situation, and do it nicely. I have handed the paper and figure 1 out to my students already. For figure 1, it is mainly dealing with normally distributed data (or where one seeks to transform the data to be normally distributed). After reading the abstract I was hoping to see suggestions on how binomial data should be presented as well. At least in epidemiology it is common to use [0, 1] outcomes, and I think many researchers and students would appreciate these type of variables included in figure 1. Only a suggestion.