This paper uses simulation to explore the performance of a two-stage procedure where a preliminary Shapiro-Wilk test is used to choose between the ANOVA and Kruskal-Wallis tests as a three-sample location test. The results suggest that the two-stage procedure actually seems to be preferable when conducting such location tests.
Lantz, Björn; Andersson, Roy; and Manfredsson, Peter
"Preliminary Tests of Normality When Comparing Three Independent Samples,"
Journal of Modern Applied Statistical Methods: Vol. 15
, Article 11.
Available at: http://digitalcommons.wayne.edu/jmasm/vol15/iss2/11