Hypothesis testing
How to perform appropriate statistical tests to analyse if any difference exists between
the distributions of petal widths of the species. State your assumptions and
evidence you have to support those assumptions. (from iris dataset in R). Does anyone know how to answer to this query ?
It is helpful. Thank you 
I don't think three-way ANOVA is the answer. There is only one factor here, the species. If the null hypothesis is "the mean petal width is the same across all species", then the appropriate test is one-way ANOVA.
However, the question is about the difference between the distributions of petal widths. The appropriate test to compare distributions is a Kolmogorov-Smirnov test. It can be applied pairwise, between all pairs of species, but then a multiple test correction needs to be applied to the resulting p-values.
Framing the question is always the hardest part.
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