One Of The Assumptions For Performing An Anova F Test
According to the text, the one-way ANOVA test is robust and can tolerate violations to its normality assumption. When dealing with non-normally distributed data, an alternative approach would be the Wilcoxon rank-sum test. ANOVA is also robust against violations of normality and there are alternative approaches for designs with multiple between factors, such as Welch's ANOVA. However, ANOVA is not robust against violations of homogeneity of variances. It also assumes that the population standard deviation is the same for all groups.
If the assumption of normality is clearly violated but all other ANOVA assumptions have been met, an appropriate alternative test is the Kruskal-Wallis test. This test is a non-parametric alternative to the one-way ANOVA and is used to determine whether there are statistically significant differences between two or more groups.
The Kruskal-Wallis test is used when the assumption of normality is violated and is therefore a suitable alternative in such cases. It does not require the assumption of normality and is based on the ranks of the data values rather than their actual numerical values.
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