The normality assumption behind ANOVA and other parametric methods implies that response variables are measured on continuous scales. A simulation approach is used to explore the impact of continuity violation on the performance of statistical methods commonly used by applied researchers to compare locations across several groups.
"The Impact of Continuity Violation on ANOVA and Alternative Methods,"
Journal of Modern Applied Statistical Methods:
2, Article 6.
Available at: http://digitalcommons.wayne.edu/jmasm/vol12/iss2/6