I think these 2 previously answered questions will be very useful for you as you ponder testing for normality: (1) [how-to-choose-between-t-test-or-non-parametric-test-e-g-wilcoxon-in-small-sample][1] (2) [is-normality-testing-essentially-useless][2] [This answer][3] has some especially useful info about test selection based on your N and what the tails look like of the distribution. I would not recommend basing test selection on the results of a normality test. I would look at the data, think about your expected distribution based on the type of data you have, and follow the advice from above. [A QQ plot][4] can be helpful for 'eye-balling' if the data are approximately normal and test if a simple transformation of the data could help. [1]: http://stats.stackexchange.com/questions/121852/how-to-choose-between-t-test-or-non-parametric-test-e-g-wilcoxon-in-small-sampl [2]: http://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless [3]: http://stats.stackexchange.com/a/123389/135697 [4]: http://stats.stackexchange.com/questions/101274/how-to-interpret-a-qq-plot