I agree with Dr. Donald Myers except when he wrote :
"As yet all purported
inference tests depend on random sampling (random site selection is not
random sampling) or strong distributional assumptions such as multi-variate normality"
1) permutation or randomization tests do not need random sampling since they are performed conditionally to the data : they only need exchangeability (independence imply exchangeability, but the reverse is not always true) ;
2) what does Donald Myers want to say by "random site selection is not random sampling" ? It is necessary to specify what the population is !
If the population of interest is the set of all sites for a ReV within a given domain, then "random site selection IS random sampling". If the population is a superpopulation model (i.e. in geostatistics a two-dimensional RF) then "random site selection IS NOT random sampling" because the population is not the same as before.
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