On May 15, 2008, at 2:07 PM, lamack lamack wrote:
Dear all, someone could explain why the following example is not a
valid
randomization scheme?
Consider an experiment in which the
six experimental units to be used are permanently fixed in a row and
two treat-
ments are to be randomly assigned to the units. (One can think of
fruit trees
or a sequence of runs on a piece of laboratory equipment as the
experimental
units.) A scientist proposes using an unbiased coin to assign the
treatments. He
comes to the first unit, tosses the coin, and if it shows a head,
assigns treatment
a and otherwise, treatment b. This is repeated at the second unit,
and so on, until
three units have been assigned to one of the treatments. Then the
remaining units
are assigned to the other treatment. Show that this is not a valid
randomization
scheme.
Hm, this sounds very much like a homework. So I am going to leave you
with what I would perceive to be a hint. Presumably a valid
randomization scheme is one where each of the possible resulting
arrangements is equally likely. So all you got to do is find out why
some of them are more likely than others in your case.
best regards.
Haris Skiadas
Department of Mathematics and Computer Science
Hanover College
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