Reference for how Prism compares normal and lognormal distributions

As part of its normality tests, Prism (since version 8) can compare the fit of data to a normal (same as Gaussian) and lognormal distribution. 

Prism only fits those two distributions and gives the percentage chance that each is more likely to be the distribution from which the data were sampled. Of course, there is an infinite number of other distributions the data could be sampled from. Prism only asks which is more likely, normal or lognormal? It won't notice if neither is very likely!

Lognormal distributions are common in biology, so you'd think it would be common to ask whether data are more likely to be sampled from normal (Gaussian) or lognormal distributions. In fact, this comparison is done rarely. Prism (as of 2017) seems to be unique in making this test simple.

We use the method in section 6.7.2  of Burnham and Anderson, Model selection and multimodel inference: a practical information-theoretic approach, 2nd edition. Basically, their method fits both normal and lognormal distributions using maximum likelihood method, and then shows both likelihoods normalized to sum to 100%. They point out that this is equivalent to comparing the AIC of the two fits. If you don't have this wonderful book, here are the relevant pages (posted with Dr. Burnham's permission).

Example

Data:   11, 23, 45, 64, 31, 55, 123

Results from GraphPad Prism 8.4