Continuing the discussion started in my 2018 questions (https://www.researchgate.net/post/Is-it-permissible-to-use-standard-statistical-formulas-for-mean-and-standard-deviation-of-visual-acuity-using-LogMAR-scale and https://www.researchgate.net/post/Is-LogMAR-is-only-proper-way-to-convey-visual-acuity).

After a long break, I had the opportunity to return to this topic with the help of a data scientist. We came to the conclusion that at least one of the arguments for the widespread use of LogMAR for visual acuity (Gaussian distribution) is invalid, since the decimal representation was always closer to the best fit to Gausian than LogMAR.

At least, parametric statistical methods are more suited to the decimal VA than to LogMAR (Article Application of parametric statistics to visual acuity data

In the answers to my questions in 2018 and in the articles recommended there, one of the strongest arguments was that visual acuity tend to be Gaussian on a log-scale. We decided to test this argument on real data - a hundred healthy subjects with full ref. correction, as well as on reconstructed data from several multicenter studies.

LogMAR and decimal VA turned out to be special cases of the Tuckey ladder of powers transformation from MAR (LogMAR is for the power of 0, decimal is for the power of minus 1). This transformation, along with the similar Box Cox transformation, is used, among other things, to change the shape of a skewed distribution so that it becomes Gausian or nearly Gausian. Therefore, we used this transformation for MAR of real data with a step of 0.01 in the interval from minus 3 to plus 1 to find the "most Gaussian" distribution according to the Shapiro-Wilk test, calculation of skewness and kurtosis.

In all cases, the decimal VA turned out to be closer to the Gaussian distribution than LogMAR. At the same time, a better distribution than the decimal has always been found.

Unfortunately, it was difficult to obtain raw primary visual acuity data from large studies, and the data analysis for them was approximate. The data were reconstructed from published histograms, which is due to this rounded to 0.1 LogMAR. This affected the accuracy of the Shapiro-Wilk test, which is sensitive to repeated values. However, the positive slope in the published LogMAR graphs of these studies qualitatively confirms our conclusions.

The results do not match the generally accepted practice of using LogMAR representation of visual acuity for statistical processing. I would like to know your opinion.