🚀 go-pugleaf

      For ANOVA design applications I want info about one-dimensional
sequences of trials on each of which a single treatment is administered.
The parameters are m (number of distinct treatments), n (treatment n-gram
length), and f (frequency of occurrence of each of the m**n possible
distinct n-grams).  The constrain in the randomization is that there be
f*m**n (using Fortran notation for mult. & expon.) trials in the main
sequence, in addition to a preamble of length n-1 on which observations
of the dependent variable are not used.   The purpose is for testing
for carryover effects from previous treatments as well as direct effects
of treatments on current trials.  The simplest cases of f=1 and n=1
give ordinary random permutations of the m treatments, but the tests
envisioned for carryover effects require n > 1.
   I already have a way of generating plenty of these sequences, but
have not been able to prove whether or not the method is biased relative
to the complete sample spaces whose sizes I don't even know, except that
they are quite large in most cases of interest.
   Randomized-block and latin-square theory is too restrictive, though
Williams (1949,1950, Austr. J. Sci. Res.) and Cox (1958,p.276) used
modified latin squares for a few simple special cases.
   I know a little more about these sequences than is appropriate to
expound here, but suspect that someone must know a lot more than I do.
suggestions or references to books and journal articles would be welcome
via return posting or e-mail.
                 Phil Emerson
                 Cleveland State University