Without normality or homogeneity of variances

[LPC22]

I have four treatments. The variables to study, which are weights and lengths, do not follow a normal distribution and the groups do not have the same variance so the question is: which kind of test should I use?

[ballardw]

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@LPC22 wrote:

I have four treatments. The variables to study, which are weights and lengths, do not follow a normal distribution and the groups do not have the same variance so the question is: which kind of test should I use?

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It will help if you can tell us what your research question is. Are you testing for identical means or median? A known/suspected difference in a mean or median? Distribution of values?

[PGStats]

Non parametric tests do not rely on the normality of data for validity. Look at the documentation for proc npar1way.

[LPC22]

I thought to use Kruskal-Wallis test but data for some variables are heteroscedastic.

[PGStats]

Heteroscedasticity might not be a real problem here. Variables such as weights and lengths are typically not very skewed. ANOVA is quite robust to mild non-normality and might be perfectly fine. Heteroscedasticity will cost you some power in K-W analysis, but inferences will remain valid. Try both ANOVA and K-W. If you get similar p-values, you're fine. Otherwise, you should look more closely at your data for outliers, subgroups, etc.