I abhor Lilliefor and other tests of normality (April 14, 2005) Category: Modeling issues

Someone asked me about a log transformation for their data. It seemed like a good idea, based on my general comments on the log transformation, but the test of significance for normality (Lilliefor's test) was still rejected even after the log transformation.

In general, I dislike Lilliefor's test (and other tests of normality like the Shapiro-Wilks test). They have way too much power power for large sample sizes and will often end up detecting trivial departures from normality. Instead of a formal test, use a histogram, boxplot, normal probability plot, or whatever to get a qualitative indication of how close your data is to a normal distribution.

Further reading

• Stats: Checking the assumption of normality
• www.statit.com/support/quality_practice_tips/ normal_probability_plot_interpre.htm
• www.skymark.com/resources/tools/normal_test_plot.asp
• www.itl.nist.gov/div898/handbook/eda/section3/normprpl.htm

This webpage was written by Steve Simon and was last modified on 07/08/2008.