Advice: Don't rely solely on normality tests to decide when to perform nonparametric tests.

Some programs first perform a normality test, and use the results to suggest whether you should use a parametric or nonparametric test. Prism and InStat do not do this, because the choice of parametric vs. nonparametric is usually more complicated than that. Consider these points:

• Ideally, of course, you should choose the test before you collect any data. In this case, a normality test will not change your decision.
• When you analyze a series of experiments, you want to analyze them all the same way. Therefore results from a single normality test won't help you decide whether to use a nonparametric test.
• If the normality test concludes that the data deviate significantly from a Gaussian distribution, the problem can often be 'fixed' by transforming all the values (perhaps to their logarithm or reciprocal) or eliminating an outlier, rather than using a nonparametric test.
• The decision of whether to use a parametric or nonparametric test is most important with small data sets (since the power of nonparametric tests is so low). But with small data sets, normality tests have little power.
• With large data sets, even tiny deviaitons from the Gaussian ideal might be deemed "statistically significant" by a normality test. But t tests and ANOVA work fine even if the distribution deviates a bit from Gaussian.

The decision of when to use a parametric test and when to use a nonparametric test is a difficult one. It really is difficult, requiring thinking and perspective. This decision should not be automated.