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help about: anova and population no normal

Dear R-Helpers,

Parametric statistics are statistics where the population is assumed to fit any
parametrized distributions (most typically the normal distribution).
My problem is:
1) if my polulation is no normal 
2) if the sample data of all replications and treatments were well fitted from
the Weibull distribution (shape and scale parameters).

Can be The shape and scale parameters compared between treatments by using the
canonical analysis of the variance ANOVA?

Many thanks for your help with these questions. 

Maurizio