Non-Normal Data

Your question is far too general. The answer is yes, no, maybe. If you can tell us more about what you are doing and what tests/methods you are interested in using then perhaps I or someone else could offer some suggestions.

Just to give you some understanding of why it is too general consider the following:

1. Data – both X and Y do not have to be normal for regression, however, in order for the tests of significance to be accurate the residuals must be normally distributed.

2. t-test and ANOVA are robust with respect to non-normality, however, you can have situations where the distributions are so extreme that these tests will declare non-significance when, in fact, the reverse might be true – how non-normal – good question – no real good answers – best defense – when in doubt run the Wilcoxon-Mann-Whitney or the Kruskal-Wallace tests.

etc.

Statistical analysis is not limited to formal statistical tests. Properly executed graphics and/or summary tables are a form of analysis and may be all that you need.

For example, if you are trying to explain your choice of problems to address then the pareto is one of the tools of choice. It is a clean graphic and it allows everyone to see your data in some kind of rank order of importance – and it is a statistical summary.

You could also use a pareto to to illustrate the effects of your actions – in this case it would be two paretos – a before and an after.

If we consider the world of graphs in general then there are cases on record where the graph was the primary analysis and was used, in conjunction with summary tables, to solve a problem – a good example of this is Snow’s graphical summary of the cholera epidemic in the Broadstreet area of London back in 1854. His graph, coupled with his summary of failed attempts to find any other meaningful relationship between those who died and those who survived in that area forced all of the governments of Europe to take steps to insure water quality (remember this was 30+ years before the germ theory of disease transmission was even put forward).

If you want to explore this a bit more I’d recommend reading the three books by Tufte

1. The Visual Display of Quantitative Information
2. Visual Explanations
3. Envisioning Information

Several months ago, Breyfogle and Pyzdek had quite an interesting debate on this very subject on Quality Digest’s website. I suugest you search the term “tranform data” at: http://www.qualitydigest.com/

Robert: As always, spot on. You may also wish to plot a run chart, or control chart with 2 (or more) groups to graphically show changes. And Tufte is the grand-master of visual data representation. Back in school when we were studying the Napoleonic campaign to Russia, the Tufte graph was a very powerful graphic. Those reading this who have no idea of what I’m talking about should Google Tufte and Napoleon. Truly amazing.