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 Comparing normal and lognormal distributions

Prism compares the normal and lognormal distributions using a likelihood test, and computes the relative likelihood that the data were sampled from each. Notes:

A lognormal distribution only contains positive numbers. Negative values and zeroes are impossible in lognormal distributions. If any values are zero or negative Prism does test for lognormality.

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 are 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.

For math details, see section 6.7.2  of Burnham and Anderson, Model selection and multimodel inference: a practical information-theoretic approach, 2nd edition. Basically, Prism fits a normal or lognormal distribution using maximum likelihood method, and then compares the two likelihoods. They point out that this is equivalent to comparing the AIC of the two fits.

Don't rely entirely on the results of the likelihood comparison. Also look at the tests for normality and lognormality.

Don't forget to look at graphs of the data distribution. Use the frequency distribution analysis to plot a frequency distribution histogram. Always look at the data before looking at statistical results. Also, the normality test analysis can create two QQ plots, one assuming a normal distribution and the other assuming a lognormal distribution. A QQ plot made with the appropriate assumption should be nearly linear.

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