I responded that (a) I hate twitter, and (b) In the book we discuss the importance of transformations in bringing the data closer to a linear and additive model. With a log transform there would be nothing to claim and indeed that claim is not replicable. There are data-sets where 3 out of 547 data points drive the entire p<0.05 effect. I know that on p 15 of Gelman and Hill you say that it is often helpful to log transform all-positive data, but people selectively cite this other comment in your book to justify not transforming. They don’t cite you there, but threads like the one above do keep citing you in the NHST context. I just reviewed a paper in JML (where we published our statistical significance filter paper) by some psychologists that insist that all data be analyzed using untransformed reaction/reading times. Could you clarify your point in the next edition of your book? But it is being misused by psychologists and psycholinguists in the NHST context to justify analyzing untransformed all-positive dependent variables and then making binary decisions based on p-values. This statement of yours is not meant to be a recommendation to NHST users. Normality of errors literally gets LOWEST priority. 45-47)'s summary of key regression model assumptions. Non-normality is relatively unimportant at worst you just may lose a bit of power. You’re routinely being cited as endorsing the idea that model assumptions like normality are the least important of all in a linear model: What’s new to me is this story from Shravan Vasishth:

The above is all background it’s stuff that we’ve all said many times before. This example also gives some sense of why a log transformation won’t be perfect either, and ultimately you can fit whatever sort of model you want-but, as I said, in most cases I’ve of positive data, the log transformation is a natural starting point. Increasing prices by 2% has a much different dollar effect for a $10 item than a $1000 item. The log transformation is particularly relevant when the data vary a lot on the relative scale. For example, a treatment that increases prices by 2%, rather than a treatment that increases prices by $20. A multiplicative model on the original scale corresponds to an additive model on the log scale. The reason for log transformation is in many settings it should make additive and linear models make more sense. Validity, additivity, and linearity are typically much more important. The reason for log transforming your data is not to deal with skewness or to get closer to a normal distribution that’s rarely what we care about.

Log transformation xlstat