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I have a data set of particle sizes of grains that are ground by three different machines. I want to test which machine is the best in grinding grains (i.e. the ground particles have the same sizes or have a small variation in size). The groups have unequal numbers of samples. The data are skewed left. Which test is proper in this case. Assump that the three machines have the same diameter grinding bits.

I have tried the test in this post, but I am not sure whether it is a proper way. Also, a post-hoc test was not available in that post.

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  • $\begingroup$ Is it necessary to test whether one machine is significantly better or do you simply want to determine which machine is most likely the best? $\endgroup$
    – Ryan Volpi
    Commented Jul 2, 2020 at 14:33
  • $\begingroup$ Hi Ryan, I want to test which machine is the best. $\endgroup$
    – Hoang Le
    Commented Jul 2, 2020 at 19:38

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